| Abstract: |
| In this talk, we will introduce our recent results on the large-time behaviors of solutions to the one-dimensional compressible Navier-Stokes equations and the related compressible two-phase model with free boundaries. Specifically, for both the case of constant viscosity and the case of degenerate viscosity, we prove the decay estimates for the solutions of the models in the vacuum free boundary setting. In particular, we derive the optimal pointwise decay estimates of the density function and the mass function for the compressible Navier-Stokes equations and the two-phase model, respectively. This talk is mainly based on some joint work with Prof. Changjiang Zhu. |
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