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Entropy and Vacuum for Compressible Navier-Stokes Equations


辛周平 教授(香港中文大学)



腾讯会议 ID:411 786 869


The dynamics of the vacuum state is one of the challenging issues for viscous and heat conductive compressible fluids which are governed by the full compressible Navier-Stokes equations (CNS). In the presence of vacuum, the CNS are strongly degenerate, which lead to many new phenomena such as instantaneous and finite blow-up of entropy bounded solutions and breakdown of either the total momentum or the total energy, and great difficulties associated with both local and global well-posedness of strong solutions. In particular, since the entropt is one of the most important physical states and its equation is highly singular near vacuum, so the propagation of boundedness of the entropy in the presence of far fields vacuum is of great importance. In this talk, I will discuss some of key issues in studying the full Navier- Stokes system and present some recent results on entropy-bounded strong solutions to the CNS with both constant viscosity and heat conductivity coefficients and the degenerate case. This talk is based on joint works with Jinkai Li, Hailing Li-Yuexun Wang, and Qin Duan - Shengguo Zhu.