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 glo...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).展开更多
In this article, we study the electromagnetic fluid system in three-dimensional whole space R^3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain th...In this article, we study the electromagnetic fluid system in three-dimensional whole space R^3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the L^p-L^q estimates for the linearized equations and an elaborate energy method when the L^1-norm of the perturbation is bounded.展开更多
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)+2 种基金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)
文摘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).
基金partially supported by the National Natural Science Foundation of China(11501373,11701380,11271381)Guangdong Provincial Culture of Seedling of China(2013LYM0081)+2 种基金the Natural Science Foundation of Guangdong Province(2017A030307022,2016A0300310019,2016A030307042)the Education Research Platform Project of Guangdong Province(2014KQNCX208)the Education Reform Project of Guangdong Province(2015558)
文摘In this article, we study the electromagnetic fluid system in three-dimensional whole space R^3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the L^p-L^q estimates for the linearized equations and an elaborate energy method when the L^1-norm of the perturbation is bounded.