A regularity criterion in weak spaces to Boussinesq equations

TL;DR

This paper establishes a new regularity criterion for weak solutions to the 3D Boussinesq equations, based on a single velocity component and temperature gradient in Lorentz spaces, advancing understanding of solution smoothness conditions.

Contribution

It introduces a novel regularity criterion involving one velocity component and temperature gradient in Lorentz spaces for the Boussinesq equations.

Findings

Regularity criterion in Lorentz spaces for weak solutions

Conditions involving one velocity component and temperature gradient

Enhanced understanding of solution regularity in fluid dynamics

Abstract

In this paper, we study regularity of weak solutions to the incompressible Boussinesq equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces.