Regularity criteria for the Navier–Stokes–Landau–Lifshitz system

In this paper, we study regularity criteria for the Navier–Stokes–Landau–Lifshitz system. Using delicate estimates, the regularity criteria for smooth solution of Navier–Stokes–Landau–Lifshitz system in Besov spaces and the multiplier spaces are obtained. The Navier–Stokes–Landau–Lifshitz system is coupled system of the Navier–Stokes equation and Landau–Lifshitz system, our results generalize the related results for Navier–Stokes equation and Landau–Lifshitz system to our system.