A blowup criterion for nonhomogeneous incompressible Navier–Stokes–Landau–Lifshitz system in 2‐D

Abstract

In this paper, we investigate nonhomogeneous incompressible Navier–Stokes–Landau–Lifshitz system in two‐dimensional (2‐D). This system consists of Navier–Stokes equations coupled with Landau–Lifshitz–Gilbert equation, an evolutionary equation for the magnetization vector. We establish a blowup criterion for the 2‐D incompressible Navier–Stokes–Landau–Lifshitz system with finite positive initial density.