二维不可压缩欧拉方程的稳定连续涡斑偶极子解

IF 2.4 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2025-07-18 DOI:10.1007/s00205-025-02113-z

De Huang, Jiajun Tong

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引用次数: 0

摘要

我们严格地构造了二维不可压缩欧拉方程的第一个稳定行波解，其形式为连续涡斑偶极子，可以看作是著名的Lamb-Chaplygin偶极子的涡斑对应物。我们的构造基于一种新颖的不动点方法，该方法确定斑块边界作为某个非线性映射的不动点。得到了斑块边界的平滑性和其他性质。

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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Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation

We rigorously construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewed as the vortex-patch counterpart of the well-known Lamb–Chaplygin dipole. Our construction is based on a novel fixed-point approach that determines the patch boundary as the fixed point of a certain nonlinear map. Smoothness and other properties of the patch boundary are also obtained.

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.