Existence and regularity of rotating global solutions for the generalized surface quasi-geostrophic equations

Abstract

Motivated by the recent work of Hassainia and Hmidi [Z. Hassainia, T. Hmidi - On the {V}-states for the generalized quasi-geostrophic equations,arXiv preprint arXiv:1405.0858], we close the question of the existence of convex global rotating solutions for the generalized surface quasi-geostrophic equation for $\alpha \in [1,2)$. We also show $C^{\infty }$ regularity of their boundary for all $\alpha \in (0,2)$.

42 pages

References in corpus (3)

• Absence of splash singularities for SQG sharp fronts and the Muskat problem
• On the V-states for the generalized quasi-geostrophic equations
• A self-similar cascade of instabilities in the surface quasigeostrophic system

Cited by in corpus (16)

• Existence of corotating and counter-rotating vortex pairs for active scalar equations
• Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker-Smale models
• Uniformly rotating smooth solutions for the incompressible 2D Euler equations
• Global bifurcation of rotating vortex patches
• Kármán Vortex Street in incompressible fluid models
• Imperfect bifurcation for the quasi-geostrophic shallow-water equations
• Global Solutions of a Surface Quasi-Geostrophic Front Equation
• Large Time Decay Estimates for the Muskat Equation
• Global bifurcation for corotating and counter-rotating vortex pairs
• Strong illposedness for SQG in critical Sobolev spaces
• Existence of small loops in the Bifurcation diagram near the degenerate eigenvalues
• Vortex patches choreography for active scalar equations
• Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
• Existence and stability of smooth traveling circular pairs for the generalized surface quasi-geostrophic equation
• Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation
• Existence of stationary vortex sheets for the 2D Euler equation