I will present my recent work on uniqueness of Riemann problem consisting of two shocks for 1D isentropic Euler system. The uniqueness is guaranteed in the class of vanishing viscosity limits of solutions to the associate Navier-Stokes system, as the Bianchini-Bressan conjecture. The main idea to achieve this issue is to get a uniform stability of any large perturbations from a composite wave of two viscous shocks to the Navier-Stokes. Especially, I will explain about this main idea in a simpler context, that is, in the case of a single shock. This is based on joint works with Alexis Vasseur.
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