| Abstract: |
| In this talk, I consider a compressible viscous-dispersive Euler system in one space dimension in the context of quantum hydrodynamics. In particular, the dispersive term is due to quantum effects described through the Bohm potential, while the viscosity term is nonlinear. The main goal is to prove that small-amplitude viscous-dispersive shock profiles for the system under consideration are spectrally stable. The proof is based on spectral energy estimates, for which the monotonicity of the profiles in the small-amplitude regime plays a crucial role. This is a joint work with Ramon Plaza (UNAM) and Delyan Zhelyazov (University of Surrey). |
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