Global Existence, Uniqueness And Asymptotic Behavior Of Weak Solution To Compressible Navier-Stokes Equations With Gravity And Vacuum

In this paper, we study the free boundary problem for the one-dimensional isentropic Navier-Stokes equations with vacuum and gravity for the general pressure P = P(ρ). We mainly obtain global existence, but the uniqueness of the weak solution is mentioned. In particular, we get the result of Theorem 4.7, which shows that the time-asymptotic state corresponds to the hydrostatic pressure law.