Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain

TL;DR

This paper establishes conditions under which solutions to the 3D Boussinesq, MHD, and Landau-Lifshitz equations in bounded domains become singular, advancing understanding of their blow-up behavior.

Contribution

It provides new blow-up criteria for these complex systems within bounded domains, extending previous results to more general settings.

Findings

Derived blow-up criteria for Boussinesq, MHD, and Landau-Lifshitz equations.

Identified conditions leading to finite-time singularities in these systems.

Enhanced theoretical understanding of solution behaviors in bounded domains.

Abstract

In this paper, we prove some blow-up criteria for the 3D Boussinesq system with zero heat conductivity and MHD system and Landau-Lifshitz equations in a bounded domain.