Uniformly rotating smooth solutions for the incompressible 2D Euler equations

Abstract

In this paper, we show the existence of a family of compactly supported smooth vorticities, which are solutions of the 2D incompressible Euler equation and rotate uniformly in time and space.

58 pages

References in corpus (3)

• Existence of corotating and counter-rotating vortex pairs for active scalar equations
• On the V-states for the generalized quasi-geostrophic equations
• Symmetries and Critical Phenomena in Fluids

Cited by in corpus (12)

• Kármán Vortex Street in incompressible fluid models
• Symmetry in stationary and uniformly-rotating solutions of active scalar equations
• Global bifurcation for corotating and counter-rotating vortex pairs
• Remarks on stationary and uniformly-rotating vortex sheets: Rigidity results
• Non uniform rotating vortices and periodic orbits for the two-dimensional Euler Equations
• Vortex patches choreography for active scalar equations
• Existence and regularity of co-rotating and travelling global solutions for the generalized SQG equation
• Existence of corotating asymmetric vortex pairs for Euler equations
• Existence of co-rotating and travelling vortex patches with doubly connected components for active scalar equations
• Existence of stationary vortex sheets for the 2D Euler equation
• On Singular Vortex Patches, II: Long-time dynamics
• Co-rotating and traveling vortex sheets for the 2D incompressible Euler equation