粘性量子流体力学中驻波和行波的存在性

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2022-02-15 DOI:10.4171/zaa/1723

D. Zhelyazov

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引用次数: 3

摘要

证明了两种具有线性和非线性黏度的量子流体力学系统的驻波存在性。此外，利用合适的Lyapunov函数，证明了前者在不受黏度和色散参数限制的情况下行波的全局存在性。这是相对于\cite{LMZ2020}的全局存在结果的改进，在那里要求粘度足够强。

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Existence of standing and traveling waves in quantum hydrodynamics with viscosity

We prove existence of standing waves for two quantum hydrodynamics systems with linear and nonlinear viscosity. Moreover, global existence of traveling waves is proved for the former without restrictions on the viscosity and dispersion parameters, thanks to a suitable Lyapunov function. This is an improvement with respect to the global existence result in \cite{LMZ2020}, where it was required that the viscosity is sufficiently strong.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.