Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04414 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We prove the existence of nonradial classical solutions to the 2D incompressible Euler equations with compact support. More precisely, for any positive integer $k$, we construct compactly supported stationary Euler flows of class $C^k(\mathbb{R}^2)$ which are not locally radial. The proof uses a degree-theory-based bifurcation argument which hinges on three key ingredients: a novel approach to stationary Euler flows through elliptic equations with non-autonomous nonlinearities; a set of sharp regularity estimates for the linearized operator, which involves a potential that blows up as the inverse square of the distance to the boundary of the support; and overcoming a serious problem of loss of derivatives by the introduction of anisotropic weighted functional spaces between which the linearized operator is Fredholm.