Regularity criteria via horizontal component of velocity for the Boussinesq equations in anisotropic Lorentz spaces

In this article, we study the regularity criteria of the weak solutions to the Boussinesq equations involving the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. This result reveals that the velocity field plays a dominant role in regularity theory of the Boussinesq equations.

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In this article, the regularity criteria for weak solutions of the Boussinesq equations are studied, focusing on the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. The results highlight the dominant role of the velocity field in the regularity theory of the Boussinesq equations.