二维等温可压缩Navier-Stokes方程的端点紧性与有限能量弱解

中文摘要 AI 辅助

我们证明了在有界C²区域中，满足无滑移边界条件的二维等温可压缩Navier-Stokes方程存在有限能量重整化弱解的全局存在性。初始数据属于自然能量类，允许真空和无界密度。这解决了幂律压力经典二维有限能量重整化存在理论中等温端点γ=1的问题。我们基于中心密度振荡的与截断无关的可积界，提出了一种新的端点紧性论证，该论证在自然能量水平下得到近似密度的强L¹紧性。

英文摘要

We prove global existence of finite-energy renormalized weak solutions to the 2D isothermal compressible Navier--Stokes equations in bounded $C^2$ domains with no-slip boundary conditions. The initial data are arbitrary in the natural energy class, allowing vacuum and unbounded density. This resolves the isothermal endpoint $γ=1$ of the classical 2D finite-energy renormalized existence theory for power-law pressures. We develop a new endpoint compactness argument based on a truncation-independent integrable bound for centered density oscillations. This argument yields strong $L^1$ compactness of the approximating densities at the natural energy level.

发表机构

• Department of Mathematics, University of Florida（佛罗里达大学数学系）

机构由 AI 辅助整理，请以论文原文为准。