题目：Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum

报告人：李进开 (Jinkai Li)（香港中文大学）

摘要：The entropy is one of the fundamental states of a fluid and, in the  viscous case, the equation that it satisfies is highly singular in the region close to the vacuum. In spite of its importance in the gas dynamics, the mathematical analyses on the behavior of the entropy near the vacuum region, were rarely carried out; in particular, in the presence of vacuum, either at the far field or at some isolated interior points, it was unknown if the entropy remains its boundedness. It will be shown in this talk that the ideal gases retain their uniform boundedness of the entropy, locally or globally in time, if the vacuum occurs at the far field only and the density decays slowly enough at the far field.

Precisely, we will show that the Cauchy problem to the one-dimensional full compressible Navier-Stokes equations without heat conduction have a unique local or global entropy-bounded solutions, in the presence of vacuum at the far field only. It is also shown that, different from the case that with compactly supported initial density, the compressible Navier-Stokes equations, with slowly decaying initial density, can propagate the regularities in the inhomogeneous Sobolev spaces. This is a joint work with Professor Zhouping Xin, see [1].

[1] Jinkai Li and Zhouping Xin:  Entropy-bounded solutions to the compressible Navier-Stokes equations: with far field vacuum,  arXiv 1710.06571

时间：12月25日（周一）下午15:00-16:00

地点：首师大校本部新教二楼627

欢迎全体师生积极参加！