Incompressible Limit Of Navier-Stokes Equations With Density-dependent Viscosity

Hydrodynamics is mainly used to study the motion state and law of fluid(such as gas,liquid,etc.).Navier-Stokes equations are the most basic and important equations in hydrodynamics equations,which can be used to describe compressible or incompressible fluids.In this dissertation,mainly studies the incompressible limit of the global strong solution of Navier-Stokes equations with density-dependent viscosity.The main results are as follows:1.Firstly,we study the incompressible limit of the global strong solution of isentropic compressible Navier-Stokes equations with density-dependent viscosity in R~3,which the initial data is"well prepared"and the velocity satisfies the vorticity-slip boundary condition.The main idea is deriving the uniform energy estimate about the Mach numberεand the time t in order to get the incompressible limit of the global strong solution of the compressible Navier-Stokes equations.The difficulties of this dissertation are to carefully deal with the viscosity term related to density and to estimate of the higher-order derivative of velocity.2.Secondly,we research the incompressible limit of the global solution of non-isentropic compressible Navier-Stokes equations with density-dependent viscosity in R~3,which the velocity and temperature meet Navier-slip boundary conditions and convective boundary conditions respectively.Its main ideas and proof process are the same as those in the previous part,but it is more difficult.