圆盘上不可压缩欧拉方程的一类精确解的稳定性

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-04-15 DOI:10.1016/j.jfa.2025.110998

Guodong Wang

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引用次数: 0

摘要

我们证明了圆盘上二维不可压缩欧拉方程的一类用第一类贝塞尔函数表示的精确稳定解的尖锐轨道稳定性结果。这些解的一个特例是截断的兰姆偶极子，它的流函数对应于狄利克雷拉普拉斯函数的第二个特征函数。通过欧拉方程的守恒量和紧性论证，为这些解建立了合适的变分表征，从而实现了证明。

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Stability of a class of exact solutions of the incompressible Euler equation in a disk

We prove a sharp orbital stability result for a class of exact steady solutions, expressed in terms of Bessel functions of the first kind, of the two-dimensional incompressible Euler equation in a disk. A special case of these solutions is the truncated Lamb dipole, whose stream function corresponds to the second eigenfunction of the Dirichlet Laplacian. The proof is achieved by establishing a suitable variational characterization for these solutions via conserved quantities of the Euler equation and employing a compactness argument.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis