发表机构
University of Chinese Academy of Sciences; Southwestern University of Finance and Economics（中国科学院大学; 西南财经大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究多维退化可压缩Navier-Stokes方程，对任意大球对称初始数据建立弱解全局存在性，证明真空有限时间消失，并给出经典解的长时间行为。
AI 中文摘要
本文研究全空间或球内具有退化密度依赖粘性系数的二维和三维正压可压缩Navier-Stokes方程，初始数据为任意大的球对称数据。对于允许真空的初始数据，我们建立了弱解的全局存在性，并导出了一致时间先验估计。作为推论，我们证明了弱解的真空态将在有限时间内消失。关键要素包括基于低密度和高密度区域分离估计的压力项处理、Bresch-Desjardins熵估计、加权径向估计，以及速度和有效速度的耦合控制。在三维情形下，该方法还允许我们处理绝热指数的端点情形。对于具有严格正密度的足够正则初始数据，我们建立了经典解的全局存在性和长时间行为。
英文摘要
In this paper, we study the two- and three-dimensional barotropic compressible Navier-Stokes equations with degenerate density-dependent viscosity coefficients in the whole space or in a ball for arbitrarily large spherically symmetric initial data. For initial data allowing vacuum, we establish the global existence of weak solutions and derive uniform-in-time a priori estimates. As a consequence, we prove that the vacuum state of weak solutions will vanish in finite time. The key ingredients include a treatment of the pressure terms based on separate estimates in the low- and high-density regions, the Bresch-Desjardins entropy estimates, weighted radial estimates, and a coupled control of the velocity and effective velocity. In the three-dimensional case, this approach also allows us to treat the endpoint case of the adiabatic exponent. For sufficiently regular initial data with strictly positive density, we establish the global existence and large-time behavior of classical solutions.
