Estimates near the boundary for critical SQG

TL;DR

This paper establishes boundary estimates for the critical dissipative SQG equation in bounded domains, showing that boundary regularity depends on the scalar's boundary behavior.

Contribution

It provides the first boundary estimates for critical SQG with square root Laplacian dissipation in bounded domains, linking regularity to boundary scalar vanishing.

Findings

Global regularity depends on boundary scalar vanishing.

Boundary estimates are obtained for critical SQG.

Regularity up to the boundary is characterized by scalar behavior.

Abstract

We obtain estimates near the boundary for the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove that global regularity up to the boundary holds if and only if a certain quantitative vanishing of the scalar at the boundary is maintained.