弯曲空间中非相干流体的欧拉方程

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-04-12 DOI:10.1016/j.physd.2025.134667

B.G. Konopelchenko , G. Ortenzi

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引用次数: 0

摘要

讨论了恒压弯曲空间中欧拉方程的矢图方程。结果表明，利用测地线和相关积分的已知结果，可以构造几种类型的弦图方程。这些柱状方程为我们提供了欧拉方程的各种类型的解，包括平稳解。对三维欧几里得空间中锥和球的特殊情况进行了详细的分析。考虑了四维欧几里德空间中球上的欧拉方程。

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On Euler equation for incoherent fluid in curved spaces

Hodograph equations for the Euler equation in curved spaces with constant pressure are discussed. It is shown that the use of known results concerning geodesics and associated integrals allows to construct several types of hodograph equations. These hodograph equations provide us with various classes of solutions of the Euler equation, including stationary solutions. Particular cases of cone and sphere in the 3-dimensional Euclidean space are analysed in detail. Euler equation on the sphere in the 4-dimensional Euclidean space is considered too.

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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.