Time-asymptotic stability of generic Riemann solutions to the compressible Navier-Stokes equations

Since 1980s, the time-asymptotic stability of single wave pattern (viscous shock wave, rarefaction wave and viscous contact wave) to 1D compressible Navier-Stokes equations have been well-estabished and each wave pattern has quite different stability frameworks. Due to the incompatibility of those different stability frameworks, it is open until our works to prove the time-asymptotic stability of generic Riemann solutions, in particular, consisting of different multiple wave patterns, to compressible Navier-Stokes equations. The talk is concerned with our recent progress on the time-asymptotic stability of generic Riemann solutions to the 1D compressible isentropic/full Navier-Stokes equations. Last but not least, I will talk about our recent developments on the time-asymptotic stability of planar viscous shock wave to the multi-dimensional compressible Navier-Stokes and the time-asymptotic stability of the combination of viscous shock and rarefaction to the 1D scalar non-convex conservation laws.