Mathematics

CLC number: O175.28

Time Decay of Linearized Isentropic 2D Bipolar Navier-Stokes-Poisson System

二维线性等熵双极Navier-Stokes-Poisson方程的时间衰减

School of Mathematics, Hohai University, Nanjing 211100, Jiangsu, China

Received: 7 July 2024

Abstract

Cauchy problem for the linearized bipolar isentropic Navier-Stokes-Poisson system in ${\mathbb{R}}^{\mathrm{2}}$ is studied. Through the reformulation of unknown functions, we change the formal system into a linearized Navier-Stokes system and a unipolar Navier-Stokes-Poisson system. Based on a delicate analysis of the corresponding Green function, $L^{\mathrm{2}}$ decay estimate of the solution is obtained.

摘要

本文考虑二维空间线性等熵双极Navier-Stokes-Poisson方程的柯西问题。通过对未知函数的重组，我们把原方程组转化成线性的Navier-Stokes和单极Navier-Stokes-Poisson方程组之和。通过对相应格林函数的详细分析，得到解的$L^{\mathrm{2}}$衰减估计。