具有零热传导的二维完全可压缩Navier-Stokes方程组奇点的形成

Singularity Formation to the Two-dimensional Full Compressible Navier-Stokes Equations with Zero Heat Conduction

本文主要研究具有零热传导的完全可压缩Navier-Stokes方程组在二维有界区域上的强解的奇点的形成.对于初始密度含真空的情形,运用对数型的临界Sobolev不等式,证明了如果密度和压强有上界,则存在整体强解.

We consider the singularity formation of strong solutions to the two-dimensional full compressible Navier-Stokes equations with zero heat conduction in a bounded domain.It is shown that for the initial density allowing vacuum,the strong solution exists globally if the density and the pressure are bounded from above.Critical Sobolev inequalities of logarithmic type play a crucial role in the proof.