On the finite time blow-up of the Euler-Poisson equations in $\Bbb R^{2}$

Donghao Chae, Eitan Tadmor

Type: Article

Publication Date: 2008-01-01

Citations: 51

DOI: https://doi.org/10.4310/cms.2008.v6.n3.a13

Abstract

We prove the finite time blow-up for C 1 solutions of the attractive Euler-Poisson equations in R n , n ≥ 1, with and without background state, for a large set of 'generic' initial data.We characterize this supercritical set by tracing the spectral dynamics of the deformation and vorticity tensors.

Locations

Communications in Mathematical Sciences - View - PDF
Project Euclid (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	The finite time blow-up for the Euler-Poisson equations in $\Bbb R^n$	2008	Dongho Chae
+	Blowup for $C^1$ solutions of compressible Euler equations with time-dependent damping	2021	Jianli Liu Jingjie Wang Manwai Yuen
+	Blowup for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>solutions of the N -dimensional Euler–Poisson equations in Newtonian cosmology	2014	Manwai Yuen
+	Blow-up of Smooth Solutions to the Euler-Poisson Equations	2013	Yuexun Wang
+ PDF Chat	Blowup for the Euler and Euler–Poisson equations with repulsive forces	2010	Manwai Yuen
+	Dynamics of the incompressible Euler equations at critical regularity	2017	In‐Jee Jeong
+ PDF Chat	On global dynamics of $3$-D irrotational compressible fluids	2024	Qianxi Wang
+	The Euler equations in a critical case of the generalized Campanato space	2019	Dongho Chae Joerg Wolf
+	Blowup phenomena of solutions to Euler–Poisson equations	2003	Yinbin Deng Xiang Jianlin Tong Yang
+	Finite Time Blow-Up of Regular Solutions for Compressible Flows	2018	Xiangdi Huang Xin Zhou
+ PDF Chat	KdV Limit of the Euler–Poisson System	2013	Yan Guo Xueke Pu
+	Blowup of C^2 Solutions for the Euler Equations and Euler-Poisson Equations in R^N	2009	Manwai Yuen
+ PDF Chat	An improved local blow-up condition for Euler–Poisson equations with attractive forcing	2009	Bin Cheng Eitan Tadmor
+ PDF Chat	Vorticity blowup in compressible Euler equations in $\mathbb{R}^d, d \geq 3$	2024	Jiajie Chen
+	Blow up in finite time and dynamics of blow up solutions for the $L\sp 2$-critical generalized KdV equation	2002	Yvan Martel Franck Merle
+ PDF Chat	Infinite-Energy 2D Statistical Solutions to the Equations of Incompressible Fluids	2009	James P. Kelliher
+	Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity	2023	Michele Coghi Mario Maurelli
+	Blowup for Projected $$\mathbf {2}$$-Dimensional Rotational $${\mathbf {C}}^{2}$$ Solutions of Compressible Euler Equations	2019	Manwai Yuen
+	Quantized slow blow-up dynamics for the energy-critical corotational wave maps problem	2023	Uihyeon Jeong
+ PDF Chat	Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure	2024	Xiang Bai Changhui Tan Liutang Xue

Works That Cite This (50)

Action	Title	Year	Authors
+ PDF Chat	The Riemann problem for the main model cases of the Euler-Poisson equations	2024	L. V. Gargyants Olga Rozanova Marko K. Turzynsky
+	Blowup for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mi>C</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math> solutions of the Euler–Poisson equations of gaseous stars in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si2.gif" overflow="scroll"><mml:msup><mml:mi>R</mml:mi><mml:mi>N</mml:mi></mml:msup></mml:math>	2011	Manwai Yuen
+ PDF Chat	On well-posedness and singularity formation for the Euler–Riesz system	2021	Young-Pil Choi In-Jee Jeong
+	On the behavior of multidimensional radially symmetric solutions of the repulsive Euler–Poisson equations	2022	Olga Rozanova
+	Pulsating flows of the 2D Euler–Poisson equations	2017	Man Kam Kwong Manwai Yuen
+ PDF Chat	Mechanisms of Lagrangian Analyticity in Fluids	2019	Matthew Hernandez
+	Global solutions for the two dimensional Euler-Poisson system with attractive forcing	2020	Yongki Lee
+	Blowup for the solutions of the Euler–Poisson equations with damping	2017	Jianli Liu Yaoli Fang
+	Large time WKB approximation for multi-dimensional semiclassical Schrödinger–Poisson system	2011	Satoshi Masaki
+	The Riemann Problem for the Main Model Cases of the Euler–Poisson Equations	2024	L. V. Gargyants Olga Rozanova Marko K. Turzynsky

Works Cited by This (19)

Action	Title	Year	Authors
+ PDF Chat	Relaxation of the isothermal Euler-Poisson system to the drift-diffusion equations	2000	Stéphane Junca M. Rascle
+	The Cauchy Problem for the Euler Equations for Compressible Fluids	2002	Gui‐Qiang Chen Dehua Wang
+	Large Time Behavior of the Solutions to a Hydrodynamic Model for Semiconductors	1998	Roberto Natalini Tao Luo Zhouping Xin
+ PDF Chat	Spectral Dynamics of the Velocity Gradient Field¶in Restricted Flows	2002	Hailiang Liu Eitan Tadmor
+ PDF Chat	Critical thresholds in Euler-Poisson equations	2001	Shlomo Engelberg Hailiang Liu Eitan Tadmor
+ PDF Chat	The Euler Equations of Compressible Fluid Flow	2007	Demetrios Christodoulou
+	On the global regularity of subcritical Euler–Poisson equations with pressure	2008	Eitan Tadmor Dongming Wei
+	A non‐isentropic Euler–Poisson model for a collisionless plasma	1993	Peter A. Markowich Paola Pietra
+	Formation of singularities in the Euler and Euler-Poisson equations	1996	Shlomo Engelberg
+	Solution reguliere a temps petit pour l'equation d'euler—poisson	1993	Pascal Garnblin