Global classical solutions of
the multi-dimensional degenerate
compressible Navier-Stoke equations
with large data of spherical symmetry
报告专家：朱圣国 教授 （上海交通大学）
报告时间：6月20日（周六）9:30-10:30
报告地点：国家天元数学西南中心516
报告摘要：
A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or implosion in finite time. A formidable challenge lies in how the well-known coordinate singularity at the origin can be overcome to control the lower or upper bound of the density. In this paper, we consider viscosity coefficients that are degenerately density-dependent, as in the shallow water equations. We prove that, for general large spherically symmetric initial data with bounded positive density, solutions remain globally regular and do not develop cavitation or implosion in two and three spatial dimensions. Moreover, far-field vacuum is allowed for the initial data under consideration here.
邀请人：程建峰
