Interface Behavior of Compressible Navier--Stokes Equations with Vacuum

Tao Luo, Zhouping Xin, Tong Yang
2000 SIAM Journal on Mathematical Analysis  
In this paper, we study a one-dimensional motion of viscous gas near vacuum with (or without) gravity. We are interested in the case that the gas is in contact with the vacuum at a finite interval. This is a free boundary problem for the one-dimensional isentropic Navier-Stokes equations, and the free boundaries are the interfaces seperating the gas from vacuum, acrossing which the density changes continuously. The regularity and behavior of the solutions near the interfaces and expanding rate
more » ... f the interfaces are studied. Smoothness of the solutions is discussed. The unique convergence of the approximate solutions is also proved.
doi:10.1137/s0036141097331044 fatcat:jax7zwz5nvdz5ofm225mydi5ui