Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
Analysis of PDEs
2025-07-21 v3 Fluid Dynamics
Abstract
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.
Cite
@article{arxiv.2406.09849,
title = {Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation},
author = {De Huang and Jiajun Tong},
journal= {arXiv preprint arXiv:2406.09849},
year = {2025}
}
Comments
42 pages, 6 figures