报告题目: Local classical solutions to the Compressible Isentropic Navier-Stokes Equations with density-dependent viscosities and vacuum
报 告 人:李亚纯 教授(上海交通大学)
报告时间:2016年5月13日(周五)上午10:30-11:30
报告地点:4号楼4318室
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数学学院
2016年05月11日
报告摘要:
We investigate the Navier-Stokes equations for multi-dimensional compressible isentropic flow with vacuum appearing in some open set or at the far field. We first establish the local-in-time well-posedness of the unique regular solution to the compressible Navier-Stokes equations with density-dependent viscosities in a power law and with vacuum, whose life span is uniformly positive with respect to the viscosity coefficients. Then we prove that our regular solution will blow up in finite time under two kinds of blow-up mechanisms. Finally we consider the vanishing viscosity limit by establishing uniform energy-type estimates with respect to the viscosity coefficients for the regular solutions, which leads to the convergence of the regular solution of the Navier-Stokes equations to that of the Euler equations with arbitrarily large data with vacuum.