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Article overview
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Well-posedness and decay structure of a quantum hydrodynamics system with Bohm potential and linear viscosity | | Ramón G. Plaza
; Delyan Zhelyazov
; | | Date: |
1 Sep 2023 | | Abstract: | In this paper, a compressible viscous-dispersive Euler system in one space
dimension in the context of quantum hydrodynamics is considered. The purpose of
this study is twofold. First, it is shown that the system is locally
well-posed. For that purpose, the existence of classical solutions which are
perturbation of constant states is established. Second, it is proved that in
the particular case of subsonic equilibrium states, sufficiently small
perturbations decay globally in time. In order to prove this stability
property, the linearized system around the subsonic state is examined. Using an
appropriately constructed compensating matrix symbol in the Fourier space, it
is proved that solutions to the linear system decay globally in time,
underlying a dissipative mechanism of regularity gain type. These linear decay
estimates, together with the local existence result, imply the global existence
and the decay of perturbations to constant subsonic equilibrium states as
solutions to the full nonlinear system. | | Source: | arXiv, 2309.00175 | | Services: | Forum | Review | PDF | Favorites | |
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