Traveling waves for quantum hydrodynamics with nonlinear viscosity

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:493

Article

Lattanzio, Corrado¹  Zhelyazov, Delyan¹ 

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

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

DOI  :  10.1016/j.jmaa.2020.124503

来源: Elsevier

【 摘 要 】

In this paper we study existence of traveling waves for 1-D compressible Euler system with dispersion (which models quantum effects through the Bohm potential) and nonlinear viscosity in the context of quantum hydrodynamic models for superfluidity. The existence of profiles is proved for appropriate (super- or sub- sonic) end states defining Lax shocks for the underlying Euler system formulated in terms of density and velocity without restrictions for the viscosity and dispersion parameters. On the other hand, the interplay of the dispersion and the viscosity plays a crucial role in proving the existence of oscillatory profiles, showing in this way how the dispersion plays a significant role in certain regimes. Numerical experiments are also provided to analyze the sensitivity of such profiles with respect to the viscosity/dispersion terms and with respect to the nearness to vacuum. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free