In this paper, we investigate the global existence and uniqueness of strong solutions to the 2D anisotropic Boussinesq system for rough initial data with striated regularity. We 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 study the propagation of the striated regularity for the smooth temperature patches problem. The proofs rely on the idea of Chemin to solve the 2-D vortex patch problem for ideal fluids, namely the striated regularity can help to bound the gradient of the velocity.

中文翻译：

---

二维各向异性Boussinesq系统的条纹规律

在本文中，我们针对具有规则性的粗糙初始数据，研究了二维各向异性Boussinesq系统强解的整体存在性和唯一性。我们证明了具有各向异性热扩散的Boussinesq系统的整体适定性，其初始涡度在某些平滑界面上是不连续的。在各向异性水平粘度的情况下，我们研究了平滑温度斑问题的条纹规律性的传播。证明依赖于Chemin的思想来解决理想流体的二维涡旋斑问题，即横纹规则性可以帮助限制速度的梯度。