# On the striated regularity for the 2D anisotropic Boussinesq system

## TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 2D anisotropic Boussinesq system with striated initial data, extending the understanding of anisotropic effects in fluid dynamics.

## Contribution

It introduces a novel approach using striated regularity to establish well-posedness for anisotropic Boussinesq systems with discontinuous vorticity.

## Key findings

- Global well-posedness for anisotropic thermal diffusion cases.
- Propagation of striated regularity in temperature patches.
- Bounded velocity gradient via striated regularity.

## Abstract

In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with anisotropic thermal diffusion or anisotropic viscosity and with striated initial data. Using the key idea of Chemin to solve 2-D vortex patch of ideal fluid, namely the striated regularity can help to bound the gradient of the velocity, we can prove the global well-posedness of the Boussinesq system with anisotropic thermal diffusion with initial vorticity being discontinuous across some smooth interface. In the case of an anisotropic horizontal viscosity we can study the propagation of the striated regularity for the smooth temperature patches problem.