Long-Time Behavior towards Shock Profiles for the Navier-Stokes-Poisson System

Autor:	Kang, Moon-Jin, Kwon, Bongsuk, Shim, Wanyong
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35Q35 35C07 35B35 35B4
Druh dokumentu:	Working Paper
Popis:	We study the stability of shock profiles in one spatial dimension for the isothermal Navier-Stokes-Poisson (NSP) system, which describes the dynamics of ions in a collision-dominated plasma. The NSP system admits a one-parameter family of smooth traveling waves, called shock profiles, for a given far-field condition satisfying the Lax entropy condition. In this paper, we prove that if the initial data is sufficiently close to a shock profile in $H^2$-norm, then the global solution of the Cauchy problem tends to the smooth manifold formed by the parametrized shock profiles as time goes to infinity. This is achieved using the method of $a$-contraction with shifts, which does not require the zero mass condition. Comment: 44 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.09094 Zobrazit plný text záznamu View this record from Arxiv