On pressureless Euler equation with external force

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2024-08-08 DOI:10.1016/j.physd.2024.134317

引用次数: 0

Abstract

Hodograph equations for the $n$ -dimensional Euler equations with the constant pressure and external force linear in velocity are presented. They provide us with solutions of the Euler in implicit form and information on existence or absence of gradient catastrophes. It is shown that in even dimensions the constructed solutions are periodic in time for particular subclasses of external forces. Several particular examples in one, two and three dimensions are considered, including the case of Coriolis external force.

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关于有外力的无压欧拉方程

提出了具有恒定压力和速度线性外力的 n 维欧拉方程的霍德图方程。它们为我们提供了隐式欧拉方程的解，以及梯度灾难存在与否的信息。研究表明，在偶数维度中，对于特定的外力子类，所构建的解在时间上是周期性的。我们考虑了一维、二维和三维的几个特殊例子，包括科里奥利外力的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.