The finite time blow - up for the Euler - Poisson equations
نویسنده
چکیده
We prove the finite time blow-up for C1 solutions to the EulerPoisson equations in R, n ≥ 1, with/without background density for initial data satisfying suitable conditions. We also find a sufficient condition for the initial data such that C3 solution breaks down in finite time for the compressible Euler equations for polytropic gas flows. AMS subject classification: 35Q35, 35B30
منابع مشابه
Blow-up Conditions for Two Dimensional Modified Euler-poisson Equations
The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified EulerPoisson system with a modified Riesz transform where the singular...
متن کاملA Sharp Local Blow-up Condition for Euler-poisson Equations with Attractive Forcing
We improve the recent result of [2] proving a one-sided threshold condition which leads to finite-time breakdown of the Euler-Poisson equations in arbitrary dimension n.
متن کاملUpper-thresholds for Shock Formation in Two-dimensional Weakly Restricted Euler-poisson Equations
The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow up for some initial configurations. This paper strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional weakly restricted Euler-Poisson (WREP) system. This system can be viewed as an im...
متن کاملAn improved local blow-up condition for Euler–Poisson equations with attractive forcing
We improve the recent result of Chae and Tadmor (2008) [10] proving a one-sided threshold condition which leads to a finite-time breakdown of the Euler–Poisson equations in arbitrary dimension n. © 2009 Elsevier B.V. All rights reserved.
متن کاملFinite Time Blow-up for a Dyadic Model of the Euler Equations
We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the context of the dyadic Navier-Stokes equations with hyper-dissipation we prove finite time blow-up in the case when the dissipation degree is sufficiently small.
متن کامل