尺度临界空间中可压缩Navier-Stokes方程低马赫数极限的强收敛性

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-05-24 DOI:10.1007/s00021-025-00938-y

Shozo Ogino

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引用次数: 0

摘要

研究了全空间可压缩Navier-Stokes方程的Cauchy问题和低马赫数极限问题。在标度临界空间中，当马赫数趋于0时，速度的不可压缩部分强收敛于不可压缩Navier-Stokes方程的解。我们还证明了密度和速度的可压缩部分消失。此外，我们还推导了速度可压缩部分的时间导数在马赫数趋于0时的发散。这些证明是基于热方程的\(L^1\) -极大正则性和波动方程的Strichartz估计。

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Strong Convergence of Low Mach Number Limit for the Compressible Navier–Stokes Equations in the Scaling Critical Spaces

We consider the Cauchy problem for the compressible Navier–Stokes equations in whole space and low Mach number limit problem. In this paper, we show that the incompressible part of the velocity strongly converges to the solution of the incompressible Navier–Stokes equations as the Mach number goes to 0 in the scaling critical space. We also show that the density and the compressible part of the velocity vanish. Moreover, we derive the diverging of the time derivative of the compressible part of the velocity as Mach number goes to 0. The proofs are based on the \(L^1\)-Maximal regularity for the heat equations and the Strichartz estimates for the wave equations.

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来源期刊

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.