Rigidity Results for Finite Energy Solutions to the Stationary 2D Euler Equations
Abstract
Abstract In this paper we prove rigidity results for classical solutions to the stationary 2D Euler equations in $$\mathbb {R}^2$$ R 2 . Assuming that the velocity field has finite energy and that the stagnation set is connected, we prove that the corresponding stream function solves an autonomous semilinear elliptic equation. Under some extra conditions on the vorticity near infinity we can also prove that the streamlines are concentric circles. The proofs include several energy estimates on the behavior of the stream function at infinity, as well as an adaptation of the continuous Steiner symmetrization to our setting.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Communications in Mathematical Physics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 407
- Issue
- 8
- Publication date
- 9 July 2026
- Language
- EN