On the two-phase Navier–Stokes equations with surface tension

Jan Prüß, Gieri Simonett

Type: Article

Publication Date: 2010-10-01

Citations: 107

DOI: https://doi.org/10.4171/ifb/237

Abstract

The two-phase free boundary problem for the Navier–Stokes system is considered in a situation where the initial interface is close to a halfplane. By means of Lp -maximal regularity of the underlying linear problem we show local well-posedness of the problem, and prove that the solution, in particular the interface, becomes instantaneously real analytic.

Locations

arXiv (Cornell University) - View - PDF
Interfaces and Free Boundaries Mathematical Analysis Computation and Applications - View - PDF

Similar Works

Action	Title	Year	Authors
+	On the two-phase Navier-Stokes equations with surface tension	2009	Jan Pruess Gieri Simonett
+	On the two-phase Navier-Stokes equations with surface tension	2009	Jan Pruess Gieri Simonett
+	Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension	2010	Matthias Köhne Jan Pruess Mathias Wilke
+	Qualitative Behaviour of Solutions for the Two-Phase Navier-Stokes Equations with Surface Tension	2010	Matthias Köhne Jan Pruess Mathias Wilke
+ PDF Chat	On the global wellposedness of free boundary problem for the Navier-Stokes system with surface tension	2023	Hirokazu Saito Yoshihiro Shibata
+ PDF Chat	Strong solutions to compressible–incompressible two-phase flows with phase transitions	2020	Keiichi Watanabe
+	Strong solutions to compressible-incompressible two-phase flows with phase transitions	2018	Keiichi Watanabe
+	On the Well-Posedness of Two Fluid Interfacial Flows with Surface Tension	1993	J. Thomas Beale Thomas Y. Hou John Lowengrub
+	Analytic solutions for the two-phase Navier-Stokes equations with surface tension and gravity	2009	Jan Pruess Gieri Simonett
+ PDF Chat	Analytic Solutions for the Two-phase Navier-Stokes Equations with Surface Tension and Gravity	2011	Jan Prüß Gieri Simonett
+ PDF Chat	Qualitative behaviour of solutions for the two-phase Navier–Stokes equations with surface tension	2012	Matthias Köhne Jan Prüß Mathias Wilke
+ PDF Chat	Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness	2024	Helmut Abels Harald Garcke Andrea Poiatti
+ PDF Chat	Well-posedness of the free boundary problem in incompressible MHD with surface tension	2022	Changyan Li Hui Li
+ PDF Chat	On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension	2016	Jan Prüß Senjo Shimizu Gieri Simonett Mathias Wilke
+ PDF Chat	On the Rayleigh-Taylor instability for the two-phase Navier-Stokes equations	2010	Jan Pruess Gieri Simonett
+	Local Solvability of Free Boundary Problems for the Two-phase Navier-Stokes Equations with Surface Tension in the Whole Space	2011	Senjo Shimizu
+	A two-phase flow with a viscous and an inviscid fluid	2000	Ben Schweizer
+	Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension	2009	Jan Prüß Gieri Simonett
+ PDF Chat	Global well-posedness of unsteady motion of viscous incompressible capillary liquid bounded by a free surface	2018	Yoshihiro Shibata
+ PDF Chat	Compressible–Incompressible Two-Phase Flows with Phase Transition: Model Problem	2017	Keiichi Watanabe

Works That Cite This (101)

Action	Title	Year	Authors
+	Diffuse Interface models for incompressible binary fluids and the mass-conserving Allen-Cahn approximation	2020	Andrea Giorgini Maurizio Grasselli Hao Wu
+ PDF Chat	Weak–Strong Uniqueness for the Navier–Stokes Equation for Two Fluids with Surface Tension	2020	Julian Fischer Sebastian Hensel
+	Global well-posedness for two-phase fluid motion in the Oberbeck–Boussinesq approximation	2024	Wei Zhang Jie Fu Chengchun Hao Siqi Yang
+	Global Well-Posedness for Incompressible–Incompressible Two-Phase Problem	2020	Yoshihiro Shibata Hirokazu Saito
+	On the maximal $L_p$-$L_q$ regularity of the Stokes problem with first order boundary condition; model problems	2012	Yoshihiro Shibata Senjo Shimizu
+ PDF Chat	Stability of Equilibria for Two-Phase Flows with Soluble Surfactant	2010	Dieter Bothe Jan Prüß
+	Pressure Reconstruction for Weak Solutions of the Two-Phase Incompressible Navier--Stokes Equations with Surface Tension	2018	Helmut Abels Johannes Daube Christiane Kraus
+	Classical Well-Posedness of Free Boundary Problems in Viscous Incompressible Fluid Mechanics	2017	V. A. Solonnikov И. В. Денисова
+ PDF Chat	Local well-posedness for two-phase fluid motion in the Oberbeck-Boussinesq approximation	2023	Chengchun Hao Wei Zhang
+ PDF Chat	Free boundary problems of the incompressible Navier–Stokes equations with non-flat initial surface in the critical Besov space	2024	Takayoshi Ogawa Senjo Shimizu

Works Cited by This (46)

Action	Title	Year	Authors
+	On Quasistationary Approximation in the Problem of Motion of a Capillary Drop	1999	V. A. Solonnikov
+	On the regularity of solutions of the nonstationary Navier-Stokes equations	1980	Kyûya Masuda
+ PDF Chat	Functional calculi for linear operators in vector-valued $L^p$-spaces via the transference principle	1998	Matthias Hieber Jan Prüß
+ PDF Chat	On a free boundary problem for the Navier-Stokes equations	2007	Yoshihiro Shibata Senjo Shimizu
+	Large-Time Behavior of Viscous Surface Waves	1985	J. Thomas Beale Takaaki Nishida
+	Theory of function spaces	1983	Hans Triebel
+ PDF Chat	$H^\infty$-calculus for the sum of non-commuting operators	2007	Jan Prüß Gieri Simonett
+ PDF Chat	Analytic Solutions for the Two-phase Navier-Stokes Equations with Surface Tension and Gravity	2011	Jan Prüß Gieri Simonett
+	$L_p$-Theory for a Class of Non-Newtonian Fluids	2007	Dieter Bothe Jan Prüß
+	Solvability of the problem of evolution of an isolated volume of viscous, incompressible capillary fluid	1986	V. A. Solonnikov