Charles R. Doering

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All published works

Action	Title	Year	Authors
+	Heat transport in a hierarchy of reduced-order convection models	2022	Matthew Olson Charles R. Doering
+ PDF Chat	Steady Rayleigh–Bénard convection between no-slip boundaries	2021	Baole Wen David Goluskin Charles R. Doering
+ PDF Chat	On mix-norms and the rate of decay of correlations	2021	Bryan W Oakley Jean‐Luc Thiffeault Charles R. Doering
+ PDF Chat	Thermal convection over fractal surfaces	2020	Srikanth Toppaladoddi Andrew Wells Charles R. Doering J. S. Wettlaufer
+ PDF Chat	Steady Rayleigh–Bénard convection between stress-free boundaries	2020	Baole Wen David Goluskin Matthew LeDuc Gregory P. Chini Charles R. Doering
+ PDF Chat	Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization	2020	Matthew Olson David Goluskin William W. Schultz Charles R. Doering
+ PDF Chat	Exact relations between Rayleigh–Bénard and rotating plane Couette flow in two dimensions	2020	Bruno Eckhardt Charles R. Doering Jared P. Whitehead
+	Optimal time averages in non-autonomous nonlinear dynamical systems	2020	Charles R. Doering Andrew McMillan
+	Steady coherent convection between stress-free boundaries	2020	Baole Wen David Goluskin Matthew LeDuc Gregory P. Chini Charles R. Doering
+ PDF Chat	Absence of Evidence for the Ultimate State of Turbulent Rayleigh-Bénard Convection	2020	Charles R. Doering
+ PDF Chat	Wall-to-wall optimal transport in two dimensions	2020	Andre N. Souza Ian Tobasco Charles R. Doering
+	On mix-norms and the rate of decay of correlations	2020	Bryan W Oakley Jean‐Luc Thiffeault Charles R. Doering
+	Optimal time averages in non-autonomous nonlinear dynamical systems	2020	Charles R. Doering Andrew McMillan
+ PDF Chat	Absence of Evidence for the Ultimate Regime in Two-Dimensional Rayleigh-Bénard Convection	2019	Charles R. Doering Srikanth Toppaladoddi J. S. Wettlaufer
+ PDF Chat	On the Optimal Design of Wall‐to‐Wall Heat Transport	2019	Charles R. Doering Ian Tobasco
+	Non-local mixing	2018	Thomas J. Lutz Alejandro J. Souza Charles R. Doering Glenn R. Flierl Gregory J. Wagner
+ PDF Chat	Random walker models for durotaxis	2018	Charles R. Doering Xiaoming Mao Leonard M. Sander
+ PDF Chat	Diffusion-limited mixing by incompressible flows	2018	Christopher Miles Charles R. Doering
+	Long time behavior of the two-dimensional Boussinesq equations without buoyancy diffusion	2018	Charles R. Doering Jiahong Wu Kun Zhao Xiaoming Zheng
+ PDF Chat	Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations	2018	Diego Ayala Charles R. Doering Thilo M. Simon
+ PDF Chat	Optimal Heat Transfer and Optimal Exit Times	2018	Florence Marcotte Charles R. Doering Jean‐Luc Thiffeault W. R. Young
+	Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems	2017	Ian Tobasco David Goluskin Charles R. Doering
+	Optimal bounds and extremal trajectories for time averages in dynamical systems	2017	Ian Tobasco David Goluskin Charles R. Doering
+ PDF Chat	Resonant activation of population extinctions	2017	Christopher Spalding Charles R. Doering Glenn R. Flierl
+ PDF Chat	Optimal Wall-to-Wall Transport by Incompressible Flows	2017	Ian Tobasco Charles R. Doering
+	A Shell Model for Optimal Mixing	2017	Christopher Miles Charles R. Doering
+	Optimal bounds and extremal trajectories for time averages in dynamical systems	2017	Ian Tobasco David Goluskin Charles R. Doering
+	A MINIMUM POPULATION EXTINCTION TIME DRIVEN BY STOCHASTIC ENVIRONMENTAL FORCING	2017	Christopher Spalding Charles R. Doering Glenn R. Flierl
+	New variational bounds on convective transport. I. Formulation and analysis	2016	Ian Tobasco Andre N. Souza Charles R. Doering
+ PDF Chat	Bounds for convection between rough boundaries	2016	David Goluskin Charles R. Doering
+ PDF Chat	Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model	2016	Yen Ting Lin Charles R. Doering
+	On the growth of enstrophy in axisymmetric 3D Euler flows with swirl	2015	Diego Ayala Charles R. Doering
+	Optimizing exit times	2015	Jean‐Luc Thiffeault Florence Marcotte Charles R. Doering W. R. Young
+ PDF Chat	Transport bounds for a truncated model of Rayleigh–Bénard convection	2015	Andre N. Souza Charles R. Doering
+	Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field	2015	Basile Gallet Charles R. Doering
+ PDF Chat	Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field	2015	Basile Gallet Charles R. Doering
+	Exact two-dimensionalization of low-magnetic-Reynolds-number flows subject to a strong magnetic field	2015	Basile Gallet Charles R. Doering
+ PDF Chat	Wall to wall optimal transport	2014	Pedram Hassanzadeh Gregory P. Chini Charles R. Doering
+ PDF Chat	Bounds on Surface Stress-Driven Shear Flow	2013	George I. Hagstrom Charles R. Doering
+ PDF Chat	Erratum: “Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows” [J. Math. Phys. 53, 115611 (2012)]	2013	Evelyn Lunasin Zhi Lin Alexei Novikov Anna L. Mazzucato Charles R. Doering
+	The small-world effect is a modern phenomenon	2013	Seth A. Marvel Travis Martin Charles R. Doering David Lusseau M. E. J. Newman
+ PDF Chat	Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows	2012	Evelyn Lunasin Zhi Lin Alexei Novikov Anna L. Mazzucato Charles R. Doering
+ PDF Chat	Internal heating driven convection at infinite Prandtl number	2011	Jared P. Whitehead Charles R. Doering
+ PDF Chat	Ultimate State of Two-Dimensional Rayleigh-Bénard Convection between Free-Slip Fixed-Temperature Boundaries	2011	Jared P. Whitehead Charles R. Doering
+ PDF Chat	Optimal stirring strategies for passive scalar mixing	2011	Zhi Lin Jean‐Luc Thiffeault Charles R. Doering
+ PDF Chat	Symmetric factorization of the conformation tensor in viscoelastic fluid models	2011	Nusret Balci Becca Thomases Michael Renardy Charles R. Doering
+ PDF Chat	Variations on Kolmogorov flow: turbulent energy dissipation and mean flow profiles	2011	Bertrand Rollin Yves Dubief Charles R. Doering
+ PDF Chat	The mixing efficiency of open flows	2010	Jean‐Luc Thiffeault Charles R. Doering
+	Symmetric factorization of the conformation tensor in viscoelastic fluid models	2010	Nusret Balci Becca Thomases Michael Renardy Charles R. Doering
+	A Fast Explicit Operator Splitting Method for Passive Scalar Advection	2010	Alina Chertock Charles R. Doering Eugene Kashdan Alexander Kurganov
+ PDF Chat	Demographic stochasticity versus spatial variation in the competition between fast and slow dispersers	2010	Jack N. Waddell Leonard M. Sander Charles R. Doering
+ PDF Chat	Destabilizing Taylor–Couette flow with suction	2010	Basile Gallet Charles R. Doering E. A. Spiegel
+	Demographic Fluctuations versus Spatial Variation in the Competition between Fast and Slow Dispersers	2010	Jack N. Waddell Leonard M. Sander Charles R. Doering
+	A new diagnostic for the relative accuracy of Euler codes	2010	Charles R. Doering John Gibbon Darryl D. Holm
+	Models and measures of mixing and effective diffusion	2010	Zhi Lin Katarína Boďová Charles R. Doering
+	Demographic Fluctuations versus Spatial Variation in the Competition between Fast and Slow Dispersers	2010	Jack N. Waddell Leonard M. Sander Charles R. Doering
+	Symmetric factorization of the conformation tensor in viscoelastic fluid models	2010	Nusret Balci Becca Thomases Michael Renardy Charles R. Doering
+ PDF Chat	Extreme vorticity growth in Navier–Stokes turbulence	2009	Jörg Schumacher Bruno Eckhardt Charles R. Doering
+ PDF Chat	Comparison of Turbulent Thermal Convection between Conditions of Constant Temperature and Constant Flux	2009	Hans Johnston Charles R. Doering
+	The 3D Navier-Stokes Problem	2008	Charles R. Doering
+ PDF Chat	Mixing effectiveness depends on the source–sink structure: simulation results	2008	Takahide Okabe Bruno Eckhardt Jean‐Luc Thiffeault Charles R. Doering
+ PDF Chat	DREAMS VERSUS REALITY: PLENARY DEBATE SESSION ON QUANTUM COMPUTING	2008	Derek Abbott Charles R. Doering Carlton M. Caves Daniel Lidar Howard E. Brandt A. R. Hamilton D. K. Ferry Julio Gea-Banacloche Sergey M. Bezrukov László B. Kish
+	Limits on enstrophy growth for solutions of the three-dimensional Navier-Stokes equations	2008	Lu Lu Charles R. Doering
+	Enstropy Generation and Regularity of Solutions to the 3D Navier-Stokes Equations	2007	Charles R. Doering Lu Lu
+	Mathematical Geophysics: An Introduction to Rotating Fluids and the Navier-Stokes Equations. By J.-Y. Chemin, B. Desjardins, I. Gallagher & E. Grenier. Oxford University Press, 2006. 272 pp. ISBN 019857133X. £47	2007	Charles R. Doering
+ PDF Chat	Energy dissipation in fractal-forced flow	2007	Alexey Cheskidov Charles R. Doering Nikola P. Petrov
+ PDF Chat	Stirring up trouble: Multi-scale mixing measures for steady scalar sources	2007	Tiffany A. Shaw Jean‐Luc Thiffeault Charles R. Doering
+ PDF Chat	Multiscale mixing efficiencies for steady sources	2006	Charles R. Doering Jean‐Luc Thiffeault
+ PDF Chat	Energy and enstrophy dissipation in steady state 2d turbulence	2006	Alexandros Alexakis Charles R. Doering
+	Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection	2006	Charles R. Doering Félix Otto Maria G. Reznikoff
+ PDF Chat	Links between dissipation, intermittency, and helicity in the GOY model revisited	2006	John C. Bowman Charles R. Doering Bruno Eckhardt Jahanshah Davoudi Malcolm Roberts Jörg Schumacher
+ PDF Chat	Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers	2006	Charles R. Doering Bruno Eckhardt Jörg Schumacher
+	Failure of energy stability in Oldroyd-B fluids at arbitrarily low Reynolds numbers	2006	Charles R. Doering Bruno Eckhardt Jörg Schumacher
+	Multiscale mixing efficiencies for passive scalars	2005	Jean‐Luc Thiffeault Tiffany A. Shaw Charles R. Doering
+	Bounds on the enstrophy growth rate for solutions of the 3-d Navier-Stokes equations	2005	Lu Lu Charles R. Doering
+ PDF Chat	On Travelling Waves for the Stochastic Fisher–Kolmogorov–Petrovsky–Piscunov Equation	2005	Joseph G. Conlon Charles R. Doering
+	A numerical method for some stochastic differential equations with multiplicative noise	2005	Charles R. Doering Khachik Sargsyan Peter Smereka
+ PDF Chat	Intermittency and Regularity Issues in 3D Navier-Stokes Turbulence	2005	John Gibbon Charles R. Doering
+	Mean Extinction Time for Birth-Death Processes & Failure of the Fokker-Planck Approximation	2005	Charles R. Doering Khachik Sargsyan Leonard M. Sander
+ PDF Chat	Low-Wavenumber Forcing and Turbulent Energy Dissipation	2005	Charles R. Doering Nikola P. Petrov
+ PDF Chat	Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker--Planck Approximation	2005	Charles R. Doering Khachik Sargsyan Leonard M. Sander
+ PDF Chat	Variational bounds on the energy dissipation rate in body-forced shear flow	2005	Nikola P. Petrov Lipeng Lu Charles R. Doering
+ PDF Chat	A bound on mixing efficiency for the advection–diffusion equation	2004	Jean‐Luc Thiffeault Charles R. Doering John Gibbon
+ PDF Chat	Bounds on convection driven by internal heating	2004	Lu Lu Charles R. Doering F. H. Busse
+ PDF Chat	Macrophage response to Mycobacteriumtuberculosis infection	2004	David Gammack Charles R. Doering Denise E. Kirschner
+	Extinction times for birth-death processes: exact results, continuum asymptotics, and the failure of the Fokker-Planck approximation	2004	Charles R. Doering Khachik Sargsyan Leonard M. Sander
+	Low-wavenumber forcing and turbulent energy dissipation	2004	Charles R. Doering Nikola P. Petrov
+	A Bound on Mixing Efficiency for the Advection-Diffusion Equation	2003	Jean‐Luc Thiffeault Charles R. Doering John Gibbon
+ PDF Chat	Energy dissipation in body-forced plane shear flow	2003	Charles R. Doering Bruno Eckhardt Jürgen Schumacher
+ PDF Chat	Bounds on Turbulent Transport	2003	J. A. Whitehead F. H. Busse Louis N. Howard Charles R. Doering Peter Constantin
+	Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality	2003	Charles R. Doering Carl Mueller Peter Smereka
+	Intermittency in solutions of the three-dimensional Navier–Stokes equations	2003	John Gibbon Charles R. Doering
+	Bounds on moments of the energy spectrum for weak solutions of the three-dimensional Navier–Stokes equations	2002	Charles R. Doering John Gibbon
+	Bulk Dissipation in Shear Layers with Suction	2001	Charles R. Doering Rodney A. Worthing E. A. Spiegel
+ PDF Chat	Dynamically stretched vortices as solutions of the 3D Navier–Stokes equations	1999	John Gibbon A. S. Fokas Charles R. Doering
+ PDF Chat	Infinite Prandtl Number Convection	1999	Peter Constantin Charles R. Doering
+	Attractor dimension estimates for two-dimensional shear flows	1998	Charles R. Doering Xiaoming Wang
+ PDF Chat	Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets	1998	Charles R. Doering Lubomira A. Dontcheva Małgorzata M. Kłosek
+	Energy stability bounds on convective heat transport:mNumerical study	1997	Charles R. Doering James M. Hyman
+	Rigorous estimates of small scales in turbulent flows	1996	Peter Constantin Charles R. Doering Edriss S. Titi
+	Fluctuations and Stability of Fisher Waves	1995	Jason Riordan Charles R. Doering Daniel ben‐Avraham
+	Exponential decay rate of the power spectrum for solutions of the Navier–Stokes equations	1995	Charles R. Doering Edriss S. Titi
+	Ladder results for the Navier-Stokes equations	1995	Charles R. Doering John Gibbon
+	Exponential decay of the Fourier power spectrum	1995	Charles R. Doering John Gibbon
+	Regularity and length scales for the 2<i>d</i> and 3<i>d</i> Navier-Stokes equations	1995	Charles R. Doering John Gibbon
+	Variational bounds in dissipative systems	1995	Peter Constantin Charles R. Doering
+	Weak and strong solutions of the complex Ginzburg-Landau equation	1994	Charles R. Doering John Gibbon C. David Levermore
+ PDF Chat	Crossover from rate-equation to diffusion-controlled kinetics in two-particle coagulation	1993	Vladimir Privman Charles R. Doering H. L. Frisch
+ PDF Chat	Length scales in solutions of the Navier-Stokes equations	1993	Michele V. Bartuccelli Charles R. Doering John Gibbon Simon J. A. Malham
+	Weak and Strong Turbulence in the CGL Equation	1993	John Gibbon Michele V. Bartuccelli Charles R. Doering
+	Fluctuations and correlations in a diffusion-reaction system: Unified description of internal fluctuations and external noise	1992	Werner Horsthemke Charles R. Doering Tane S. Ray Martin A. Burschka
+	Fluctuations and correlations in a diffusion-reaction system: Exact hydrodynamics	1991	Charles R. Doering Martin A. Burschka Werner Horsthemke
+	Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain	1991	Michele V. Bartuccelli Charles R. Doering John Gibbon
+	Note on the Constantin-Foias-Temam attractor dimension estimate for two-dimensional turbulence	1991	Charles R. Doering John Gibbon
+	Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition	1990	Daniel ben‐Avraham Martin A. Burschka Charles R. Doering
+	On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation	1990	Michele V. Bartuccelli Peter Constantin Charles R. Doering John Gibbon Magnus Gisselfält
+	Long crossover times in a finite system	1990	Charles R. Doering Martin A. Burschka
+	Hard turbulence in a finite dimensional dynamical system?	1989	Michele V. Bartuccelli Peter Constantin Charles R. Doering John Gibbon Magnus Gisselfält
+	Mean Exit times for Particles Driven by Weakly Colored Noise	1989	Patrick S. Hagan Charles R. Doering C. David Levermore
+	Diffusion-limited coagulation in the presence of particle input: Exact results in one dimension	1989	Charles R. Doering Daniel ben‐Avraham
+	Interparticle distribution functions and rate equations for diffusion-limited reactions	1988	Charles R. Doering Daniel ben‐Avraham
+	Equilibrium of two-species annihilation with input	1988	Daniel ben‐Avraham Charles R. Doering
+	Nonlinear parabolic stochastic differential equations with additive colored noise onR d �R +: A regulated stochastic quantization	1987	Charles R. Doering
+	A stochastic partial differential equation with multiplicative noise	1987	Charles R. Doering
+	Comment on first-passage times for processes driven by dichotomous fluctuations	1987	Charles R. Doering
+	The Positivity of the Jacobi Operator on Configuration Space and Phase Space	1984	Charles R. Doering C. Dewitt-Morette

Common Coauthors

Coauthor	Papers Together
John Gibbon	17
Jean‐Luc Thiffeault	12
David Goluskin	8
Bruno Eckhardt	7
Leonard M. Sander	7
Ian Tobasco	7
Peter Constantin	6
Michele V. Bartuccelli	5
Daniel ben‐Avraham	5
Khachik Sargsyan	4
Jörg Schumacher	4
Nikola P. Petrov	4
Basile Gallet	4
Martin A. Burschka	4
Lu Lu	3
Jared P. Whitehead	3
Gregory P. Chini	3
Andre N. Souza	3
Glenn R. Flierl	3
Becca Thomases	3
Baole Wen	3
Michael Renardy	3
Nusret Balci	3
Jack N. Waddell	3
Zhi Lin	2
Matthew LeDuc	2
J. S. Wettlaufer	2
Werner Horsthemke	2
F. H. Busse	2
Florence Marcotte	2
Edriss S. Titi	2
C. David Levermore	2
Matthew Olson	2
Diego Ayala	2
Magnus Gisselfält	2
Srikanth Toppaladoddi	2
Tiffany A. Shaw	2
Evelyn Lunasin	2
Christopher Miles	2
W. R. Young	2
E. A. Spiegel	2
Alexei Novikov	2
Bryan W Oakley	2
Christopher Spalding	2
Zhi Lin	2
Anna L. Mazzucato	2
Peter Smereka	2
Kun Zhao	1
Thomas J. Lutz	1
Jürgen Schumacher	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Ultimate State of Two-Dimensional Rayleigh-Bénard Convection between Free-Slip Fixed-Temperature Boundaries	2011	Jared P. Whitehead Charles R. Doering	12
+	Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Bénard convection	2006	Charles R. Doering Félix Otto Maria G. Reznikoff	10
+	On Howard's upper bound for heat transport by turbulent convection	1969	F. H. Busse	10
+ PDF Chat	Stirring up trouble: Multi-scale mixing measures for steady scalar sources	2007	Tiffany A. Shaw Jean‐Luc Thiffeault Charles R. Doering	9
+ PDF Chat	Energy dissipation in body-forced plane shear flow	2003	Charles R. Doering Bruno Eckhardt Jürgen Schumacher	9
+	On the dimension of the attractors in two-dimensional turbulence	1988	Peter Constantin Ciprian Foiaş Roger Témam	7
+ PDF Chat	Optimal stirring strategies for passive scalar mixing	2011	Zhi Lin Jean‐Luc Thiffeault Charles R. Doering	7
+ PDF Chat	Deterministic Nonperiodic Flow	1963	Edward N. Lorenz	6
+ PDF Chat	Using multiscale norms to quantify mixing and transport	2012	Jean‐Luc Thiffeault	6
+ PDF Chat	Multiscale mixing efficiencies for steady sources	2006	Charles R. Doering Jean‐Luc Thiffeault	6
+ PDF Chat	Heat transport by coherent Rayleigh-Bénard convection	2015	Fabian Waleffe Anakewit Boonkasame Leslie Smith	6
+ PDF Chat	Optimal heat transport solutions for Rayleigh–Bénard convection	2015	David Sondak Leslie Smith Fabian Waleffe	6
+ PDF Chat	A bound on mixing efficiency for the advection–diffusion equation	2004	Jean‐Luc Thiffeault Charles R. Doering John Gibbon	6
+	A bound on scalar variance for the advection–diffusion equation	2006	S. C. PLASTING W. R. Young	6
+	Time averaged energy dissipation rate for shear driven flows in	1997	Xiaoming Wang	6
+	Interparticle distribution functions and rate equations for diffusion-limited reactions	1988	Charles R. Doering Daniel ben‐Avraham	6
+ PDF Chat	Wall to wall optimal transport	2014	Pedram Hassanzadeh Gregory P. Chini Charles R. Doering	6
+	Bounds on dissipation for Navier–Stokes flow with Kolmogorov forcing	2001	Stephen Childress Rich R. Kerswell Andrew D. Gilbert	5
+ PDF Chat	On the smallest scale for the incompressible Navier-Stokes equations	1989	William D. Henshaw H.- Kreiss Luis G. Reyna	5
+	Smallest scale estimates for the Navier-Stokes equations for incompressible fluids	1990	William D. Henshaw H.- Kreiss Luis G. Reyna	5
+ PDF Chat	Infinite Prandtl Number Convection	1999	Peter Constantin Charles R. Doering	5
+	On the possibility of soft and hard turbulence in the complex Ginzburg-Landau equation	1990	Michele V. Bartuccelli Peter Constantin Charles R. Doering John Gibbon Magnus Gisselfält	5
+ PDF Chat	Comparison of Turbulent Thermal Convection between Conditions of Constant Temperature and Constant Flux	2009	Hans Johnston Charles R. Doering	5
+	Statics and dynamics of a diffusion-limited reaction: Anomalous kinetics, nonequilibrium self-ordering, and a dynamic transition	1990	Daniel ben‐Avraham Martin A. Burschka Charles R. Doering	5
+ PDF Chat	Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection	2009	Guenter Ahlers Siegfried Großmann Detlef Lohse	4
+ PDF Chat	Internally Heated Convection and Rayleigh-Bénard Convection	2015	David Goluskin	4
+	Interacting Particle Systems	2016	Thomas M. Liggett	4
+	Gevrey class regularity for the solutions of the Navier-Stokes equations	1989	Ciprian Foiaş Roger Témam	4
+	Simplified models for turbulent diffusion: Theory, numerical modelling, and physical phenomena	1999	Andrew J. Majda Peter R. Kramer	4
+	Ladder theorems for the 2D and 3D Navier-Stokes equations on a finite periodic domain	1991	Michele V. Bartuccelli Charles R. Doering John Gibbon	4
+ PDF Chat	Lower bounds on the mix norm of passive scalars advected by incompressible enstrophy-constrained flows	2014	Gautam Iyer Alexander Kiselev Xiaoqian Xu	4
+	Particle–antiparticle annihilation in diffusive motion	1983	D. Toussaint Frank Wilczek	4
+ PDF Chat	Variational bounds on the energy dissipation rate in body-forced shear flow	2005	Nikola P. Petrov Lipeng Lu Charles R. Doering	4
+	Blow-up in Nonlinear Schroedinger Equations-I A General Review	1986	J. Juul Rasmussen Kristoffer Rypdal	4
+	Exact solutions for a diffusion-reaction process in one dimension	1988	John L. Spouge	4
+ PDF Chat	Improved variational principle for bounds on energy dissipation in turbulent shear flow	1997	Rolf Nicodemus Siegfried Großmann Martin Holthaus	4
+	Handbook of Mathematical Functions	1966	Donald A. McQuarrie	4
+ PDF Chat	Clustering and Dispersion Rates for Some Interacting Particle Systems on $\mathbb{Z}$	1980	Maury Bramson David Griffeath	4
+	Partial regularity of suitable weak solutions of the navier‐stokes equations	1982	Luis Caffarelli Robert V. Kohn Louis Nirenberg	4
+	Asymptotic Behavior of Densities in Diffusion-Dominated Annihilation Reactions	1988	Maury Bramson Joel L. Lebowitz	4
+	Bounds on energy flux for finite energy turbulence	1975	P. L. Sulem U. Frisch	4
+ PDF Chat	Optimizing the source distribution in fluid mixing	2007	Jean‐Luc Thiffeault Grigorios A. Pavliotis	4
+	Spectral Methods for Incompressible Viscous Flow	2002	R. Peyret	3
+ PDF Chat	Topics in Optimal Transportation	2003	Cédric Villani	3
+	Concentration fluctuations in reaction kinetics	1985	G. Zumofen A. Blumen J. Klafter	3
+ PDF Chat	Particles and fields in fluid turbulence	2001	Gregory Falkovich Krzysztof Gawędzki Massimo Vergassola	3
+	Steady-state segregation in diffusion-limited reactions	1988	Katja Lindenberg Bruce J. West Raoul Kopelman	3
+ PDF Chat	Interfacial velocity corrections due to multiplicative noise	1999	Leonid Pechenik Herbert Levine	3
+	Exponential decay rate of the power spectrum for solutions of the Navier–Stokes equations	1995	Charles R. Doering Edriss S. Titi	3
+ PDF Chat	Front propagation: Precursors, cutoffs, and structural stability	1998	David A. Kessler Zvi Ner Leonard M. Sander	3