Asymptotic stability of the stationary wave for the quantum Navier-Stokes-Poisson system

被引：4

作者：

Wu, Qiwei ^{[1
]}

Hou, Xiaofeng ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2023年 / 69卷

关键词：

Quantum Navier-Stokes-Poisson system; Asymptotic behavior; Cauchy problem; Stationary wave; Energy method; LARGE TIME BEHAVIOR; UNIPOLAR HYDRODYNAMIC MODEL; QUASI-NEUTRAL LIMIT; OPTIMAL DECAY-RATE; GLOBAL EXISTENCE; EQUATIONS; CONVERGENCE;

D O I：

10.1016/j.nonrwa.2022.103713

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We shall investigate the asymptotic behavior of solutions to the Cauchy prob-lem for the three-dimensional quantum Navier-Stokes-Poisson system. We first establish the stationary wave, then by means of the energy method, we show that the smooth solutions to the Cauchy problem exist uniquely and globally, and time-asymptotically converge to the stationary wave when the initial perturbation around the stationary wave is small enough. Finally, based on the detailed analysis for the corresponding linear problem and the energy estimates for the nonlinear system, the L-2-decay rate of the solution toward the stationary wave is also obtained. (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：24

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