%0 Journal Article
%T 带最大密度限制的Navier-Stokes方程的耗散测度值解<br>Dissipative Measure-Valued Solution of Na-vier-Stokes Equation with Maximum Density Constraint
%A 李婷婷
%A 华嘉乐
%J Advances in Applied Mathematics
%P 2263-2273
%@ 2324-8009
%D 2023
%I Hans Publishing
%R 10.12677/AAM.2023.125231
%X 本文研究具有最大密度限制的可压Navier-Stokes方程，其中，最大密度限制是由一个奇性的压强项给定的。利用带有参数K的Brenner模型，我们构造了Navier-Stokes方程的逼近解。为了处理压强的奇性，引入一个逼近压强p<sup>θ,δ</sup>，其中<span>θ,δ</span>为逼近参数。当这些参数K,<span>θ,δ</span>→0时，我们证明逼近解收敛到Navier- Stokes方程的耗散测度值解。<br />
This paper considers the compressible Navier-Stokes equation with maximum density constraint, where the maximum density constraint is imposed by a singular pressure term. Approximate solu-tions of the Navier-Stokes equation are constructed using the Brenner model with a parameter K. To deal with the singularity of pressure, an approximate pressure <span>p</span><sup>θ,δ</sup> is introduced, where <span>θ,δ</span> are the approximate parameters. When <span>K,</span><span>θ,δ</span><span>→0</span> , we show that the approximate solutions con-verge to the dissipative measure-valued solution of the Navier-Stokes equation.
%K 可压Navier-Stokes方程，弱解，最大密度限制，耗散测度值解<br>Compressible Navier-Stokes Equation
%K Weak Solution
%K Maximum Density Constraint
%K Dissipative Measure-Valued Solution
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=65863