带真空的可压缩原始方程的能量等式

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-08-25 DOI:10.1007/s00021-025-00970-y

šárka Nečasová, María Ángeles Rodríguez-Bellido, Tong Tang

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引用次数: 0

摘要

研究了具有退化黏性的可压缩原始方程（CPE）系统弱解的能量守恒问题。得到了能量方程弱解的正则性的充分条件，即使解中可能包含真空。本文给出了两个定理，第一个定理给出了经典各向同性Sobolev和Besov空间中的正则性。第二种描述了各向异性空间中的规律性。由于CPE系统的特殊结构，我们在第二定理中得到了与可压缩Navier-Stokes方程不同的新的正则性结果。

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Energy Equality for the Compressible Primitive Equations with Vacuum

The paper deals with the problem of the energy conservation for the weak solutions to the compressible Primitive Equations (CPE) system with degenerate viscosity. The sufficient conditions on the regularity of weak solutions for the energy equality are obtained even for the case when the solutions may include vacuum. In this paper, we show two theorems, the first one gives regularity in the classical isotropic Sobolev and Besov spaces. The second one states regularity in the anisotropic spaces. We obtain new regularity results in the second theorem due to the special structure of CPE system, which are in contrast to compressible Navier-Stokes 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.