A sharp time-weighted inequality for the compressible Navier-Stokes-Poisson system in the critical Lp framework

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Shi, Weixuan¹  Xu, Jiang¹ 

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211106, Jiangsu, Peoples R China

关键词: Compressible Navier-Stokes-Poisson system;    Decay estimates;    Critical Besov spaces;   

DOI  :  10.1016/j.jde.2018.11.005

来源: Elsevier

【 摘 要 】

The compressible Navier-Stokes-Poisson system takes the form of usual Navier-Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electrostatic potential force. In this paper, we focus on the large-time behavior of global strong solutions in the L-p critical Besov spaces. Inspired by the dissipative effect arising from Poisson potential, we formulate a new regularity assumption of low frequencies and then establish the sharp time-weighted inequality, which leads to the optimal time-decay estimates of strong solutions. Indeed, we see that the decay of density is faster at the half rate than that of velocity, which is a different ingredient in comparison with the situation of compressible Navier-Stokes equations. Our proof mainly depends on tricky and non classical Besov product estimates with respect to various Sobolev embeddings. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free