摘要
In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek(SCHONBEK, M. E. L2decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222(1985)) under an additional assumption that the initial perturbation is bounded in L1(R3).
In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish the global solutions with the help of an energy method. Furthermore, we obtain the time decay rates of the higher-order spatial derivatives of the solutions by applying a Fourier splitting method introduced by Schonbek(SCHONBEK, M. E. L^2 decay for weak solutions of the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 88, 209–222(1985)) under an additional assumption that the initial perturbation is bounded in L^1(R^3).
基金
supported by the National Natural Science Foundation of China(Nos.11501373,11701380,and 11271381)
the Natural Science Foundation of Guangdong Province(Nos.2017A030307022,2016A030310019,and 2016A030307042)
the Guangdong Provincial Culture of Seedling of China(No.2013LYM0081)
the Education Research Platform Project of Guangdong Province(No.2014KQNCX208)
the Education Reform Project of Guangdong Province(No.2015558)
