| Abstract: |
| In this talk, we present some results of vanishing viscosity limits for the free boundary problem of compressible isentropic flows. For the free boundary compressible Navier-Stokes equations of Newtonian fluids with or without surface tension, we established the uniform regularities of solutions in Sobolev conormal and Lipschitz spaces, and justified the vanishing viscosity and surface tension limits by a strong convergence argument. On the other hand, for the free boundary compressible viscoelastic equations of neo-Hookean fluids with or without surface tension, we obtained the uniform Sobolev regularities of solutions and proved the vanishing viscosity limits in Sobolev spaces, which indicates the stabilizing effect of elasticity. |
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