# Hölder Regularity up to the Boundary for Critical SQG on Bounded Domains

@article{Stokols2019HlderRU, title={H{\"o}lder Regularity up to the Boundary for Critical SQG on Bounded Domains}, author={Logan F. Stokols and Alexis F. Vasseur}, journal={Archive for Rational Mechanics and Analysis}, year={2019}, volume={236}, pages={1543-1591} }

We consider the dissipative SQG equation in bounded domains, first introduced by Constantin and Ignatova in 2016. We show global Hölder regularity up to the boundary of the solution, with a method based on the De Giorgi techniques. The boundary introduces several difficulties. In particular, the Dirichlet Laplacian is not translation invariant near the boundary, which leads to complications involving the Riesz transform.

## 7 Citations

### Estimates Near the Boundary for Critical SQG

- MathematicsAnnals of PDE
- 2020

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…

### An application of spectral localization to the critical SQG on a ball

- MathematicsJournal of Evolution Equations
- 2022

We study the Cauchy problem for the quasi-geostrophic equations in a unit ball of the two-dimensional space with the homogeneous Dirichlet boundary condition. We show existence and uniqueness of the…

### On analyticity up to the boundary for critical quasi-geostrophic equations

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- 2021

We study the Cauchy problem for the quasi-geostrophic equations with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global…

### Emergence of time periodic solutions for the generalized surface quasi-geostrophic equation in the disc

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- 2022

. In this paper we address the existence of time periodic solutions for the generalized inviscid SQG equation in the unit disc with homogeneous Dirichlet boundary condition when α ∈ (0 , 1) . We show…

### Potential theory for drift diffusion equations with critical diffusion and applications to the dissipative SQG equation

- Mathematics
- 2020

The purpose of this paper is to prove new regularity results for drift diffusion equations under minimal assumptions on the divergence free drift term. These results are presented as potential…

### Long-time behavior of scalar conservation laws with critical dissipation

- MathematicsAnnales de l'Institut Henri Poincaré C, Analyse non linéaire
- 2022

The critical Burgers equation $\partial_t u + u \partial_x u + \Lambda u = 0$ is a toy model for the competition between transport and diffusion with regard to shock formation in fluids. It is well…

### The 2D inviscid Boussinesq equations with fractional diffusion in bounded domain

- MathematicsNonlinear Analysis: Real World Applications

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