arXiv Analytics

Sign in

arXiv:2406.09849 [math.AP]AbstractReferencesReviewsResources

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

De Huang, Jiajun Tong

Published 2024-06-14Version 1

We 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.

Comments: 41 pages, 6 figures
Categories: math.AP, physics.flu-dyn
Subjects: 35Q31, 35C07, 76B47
Related articles: Most relevant | Search more
arXiv:2311.16736 [math.AP] (Published 2023-11-28)
A solution of 2D incompressible Euler equation with algebraic spiral roll-up in the presence of Wiener type perturbation
arXiv:2206.00543 [math.AP] (Published 2022-06-01)
Vorticity convergence from Boltzmann to 2D incompressible Euler equations below Yudovich class
arXiv:2108.06909 [math.AP] (Published 2021-08-16)
Co-rotating and traveling vortex sheets for the 2D incompressible Euler equation

Links

Toolbox