In this paper, we study the three-dimensional incompressible magnetohydrody-namic equations in a smooth bounded domains, in which the viscosity of the fluid and themagnetic diffusivity are concerned with density. The ...In this paper, we study the three-dimensional incompressible magnetohydrody-namic equations in a smooth bounded domains, in which the viscosity of the fluid and themagnetic diffusivity are concerned with density. The existence of global strong solutions isestablished in vacuum cases, provided the assumption that （｜ ｜μ（ρ0）｜｜Lp＋｜｜ v（P0）｜｜Lq＋｜｜b0｜｜L^3 ＋｜｜ρO｜｜L^∞） （p,q〉3） is small enough, there is not any smallness condition on thevelocity.展开更多
This paper concerns the Cauchy problem for compressible Navier-Stokes equations.The weak dissipative structure is explored and a new proof for the classical solutions are shown to exist globally in time if the initial...This paper concerns the Cauchy problem for compressible Navier-Stokes equations.The weak dissipative structure is explored and a new proof for the classical solutions are shown to exist globally in time if the initial data is sufficiently small.展开更多
In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations. We wil...In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations. We will prove global existence of the smooth solution to the incompressible Navier-Stokes-Landau-Lifshitz equation with small initial data in T2or R2and R3.展开更多
基金supported by NSFC(11701240)the Natural Science Foundation of Jiangxi Province(2017BAB211001)
文摘In this paper, we study the three-dimensional incompressible magnetohydrody-namic equations in a smooth bounded domains, in which the viscosity of the fluid and themagnetic diffusivity are concerned with density. The existence of global strong solutions isestablished in vacuum cases, provided the assumption that （｜ ｜μ（ρ0）｜｜Lp＋｜｜ v（P0）｜｜Lq＋｜｜b0｜｜L^3 ＋｜｜ρO｜｜L^∞） （p,q〉3） is small enough, there is not any smallness condition on thevelocity.
基金The Young Excellent Teacher Program Foundation of Shanghai
文摘This paper concerns the Cauchy problem for compressible Navier-Stokes equations.The weak dissipative structure is explored and a new proof for the classical solutions are shown to exist globally in time if the initial data is sufficiently small.
基金supported by the National Natural Science Foundation of China(No.11801107)Science and Technology Projects in Guangzhou(No.202102010467)+1 种基金the second author is supported by the National Natural Science Foundation of China(Grant No.11971400)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020A1515011019)。
文摘In this paper, we will investigate the incompressible Navier-Stokes-Landau-Lifshitz equations, which is a system of the incompressible Navier-Stokes equations coupled with the Landau-Lifshitz-Gilbert equations. We will prove global existence of the smooth solution to the incompressible Navier-Stokes-Landau-Lifshitz equation with small initial data in T2or R2and R3.
