# Local and global strong solutions for SQG in bounded domains

## TL;DR

This paper establishes local and global existence results for the SQG equation in bounded domains, depending on the presence and strength of dissipation and the size of initial data.

## Contribution

It proves local well-posedness in bounded domains and demonstrates global existence of strong solutions under various dissipation and data size conditions.

## Key findings

- Local well-posedness for inviscid SQG in bounded domains
- Global existence with fractional dissipation for small data
- Global existence with arbitrary data in subcritical cases

## 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.