Dispersive shocks in quantum hydrodynamics with viscosity

PHYSICA D-NONLINEAR PHENOMENA

卷:402

Article

Lattanzio, Corrado¹  Marcati, Pierangelo²  Zhelyazov, Delyan^1,2 

[1] Univ Aquila, DISIM, Dept Informat Engn Comp Sci & Math, Laquila, Italy

[2] Gran Sasso Sci Inst, Laquila, Italy

关键词: Quantum hydrodynamics;    Traveling waves;    Spectral stability;    Dispersive-diffusive shock waves;   

DOI  :  10.1016/j.physd.2019.132222

来源: Elsevier

【 摘 要 】

In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of quantum hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm potential; moreover we introduce a (linear) viscosity to analyze its interplay with the former while proving existence, monotonicity and stability of traveling waves connecting a Lax shock for the underlying Euler system. The existence of monotone profiles is proved for sufficiently small shocks; while the case of large shocks leads to the (global) existence for an oscillatory profile, where dispersion plays a significant role. The spectral analysis of the linearized problem about a profile is also provided. In particular, we derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of the eigenvalues in the unstable plane, using a careful analysis of the Evans function. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free