Local and global strong solutions for SQG in bounded domains

Abstract

We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of ${\mathbb{R}}^2$. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical cases.

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global weak solutions for generalized SQG in bounded domains

Cited by in corpus (11)

• Global existence of quasi-stratified solutions for the confined IPM equation
• Non-uniqueness of Weak Solutions to the 3D Quasi-Geostrophic Equations
• Holder Regularity up to the Boundary for Critical SQG on Bounded Domains
• Classical Solutions for the 3D Quasi-Geostrophic System on a Bounded Domain
• On the Weak Solutions to the 3D Inviscid Quasi-Geostrophic System
• The Inviscid 3D Quasi-Geostrophic System on Bounded Domains
• Strong uniqueness principle for fractional polyharmonic operators and applications to inverse problems
• Global Existence for Nonlocal Quasilinear Diffusion Systems in Non-Isotropic Non-Divergence Form
• On the Viscous Camassa-Holm Equations with Fractional Diffusion
• Regularity of Solutions of the Camassa-Holm Equations with Fractional Laplacian Viscosity
• Non existence and strong ill-posedness in $C^k$ and Sobolev spaces for SQG