Place：Rm. N913, South Building

Abstract: The dynamics of the vacuum state is one of the challenging issues for the viscous compressible fluids. Due to the strong degeneracy of the compressible Navier-Stokes system in the presence of vacuum, there are many difficulties associated with global well-posedness of either strong or even weak solutions. This is particularly so for multi-dimensional case. Most of the past efforts have been concentrated on solutions with vacuum without entropy consideration. However, entropy is one of the most important physical states and its equation is highly singular in the presence of vacuum. 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.