Spectral stability of weak dispersive shock profiles for quantum hydrodynamics with nonlinear viscosity
arXiv:2210.16132 · doi:10.1016/j.jde.2023.02.038
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.
arXiv comment31 pages, 2 figures
References in corpus (7)
- Theory of Bose-Einstein condensation in trapped gases
- On Dispersive and Classical Shock Waves in Bose-Einstein Condensates and Gas Dynamics
- Stability of strong ideal-gas shock layers
- Stability of isentropic viscous shock profiles in the high-Mach number limit
- Shock Physics in Warm Dense Matter--a quantum hydrodynamics perspective
- On the shock wave spectrum for isentropic gas dynamics with capillarity
- Spectral stability of small-amplitude dispersive shocks in quantum hydrodynamics with viscosity