Zero Mach Number Limit Of Full Compressible Navier-Stokes-Korteweg Equations

This thesis investigates the zero mach limit of full compressible Navier-Stokes-Korteweg equations.The main results are as followsWe firstly study the case of well-prepared initial data.Under the assumptions of mall density and temperature perturbation,we use the convergence-stability principle to show that the smooth solution of full compressible Navier-Stokes-Korteweg equations converges to the solution of incompressible Navier-Stokes equations.Moreover.the convergence rate is obtained by virtue of error estimateWhen given general initial data,we derive the uniform-in-mach-number estimate of the solution of full compressible Navier-Stokes-Korteweg equations in a time-weighted Sobolev space,which give the local existence of solution.Finally,combining the uniform esitmate and the enegy decay estimate given by Metivier and Schochet,we prove the zero mach limit of full compressible Navier-Stokes-Korteweg equations.