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Abstract |
When deriving the compressible Navier-Stokes equations, the viscosity depends on the temperature and hence on the density in the isentropic case. On the other hand, The shallow water equations arisen from the 3D incompressible Navier-Stokes equations is an important example of the compressible Naver-Stokes equations with density-dependent viscosity. In this talk, we will review some recent results on the compressible Navier-Stokes equations with density-dependent viscosity, including weak solutions, classical solution, blow-up problem and so on. In particular, we will focus on the global well-posedness of classical solutions to the 2D Cauchy problem of the compressible Kazhikhov-Vaigant model with large data. Weighted energy estimates will be applied to prove our main results. |
