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- W4307787906 abstract "This paper studies the stability of weak dispersive shock profiles for a quantum hydrodynamics system in one space dimension with nonlinear viscosity and dispersive (quantum) effects due to a Bohm potential. It is shown that, if the shock amplitude is sufficiently small, then the profiles are spectrally stable. This analytical result is consistent with numerical estimations of the location of the spectrum (Lattanzio, Zhelyazov, Math. Models Methods Appl. Sci. 31, 2021). The proof is based on energy estimates at the spectral level, on the choice of an appropriate weighted energy function for the perturbations involving both the dispersive potential and the nonlinear viscosity, and on the montonicity of the dispersive profiles in the small-amplitude regime." @default.
- W4307787906 created "2022-11-05" @default.
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- W4307787906 date "2022-10-28" @default.
- W4307787906 modified "2023-09-23" @default.
- W4307787906 title "Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity" @default.
- W4307787906 doi "https://doi.org/10.48550/arxiv.2210.16132" @default.
- W4307787906 hasPublicationYear "2022" @default.
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