三维变密度不可压缩Navier-Stokes-Landau-Lifshitz方程组的整体强解

Global strong solutions of three-dimensional incompressible Navier-Stokes-Landau-Lifstz equations with variable density

研究在给定‖∇u_(0)‖L^(2)+‖Δd_(0)‖L^(2)适当小以及密度ρ可能有较大振动时,运用能量方法以及局部解的存在性和全局性先验估计,证明三维变密度不可压缩Navier-Stokes-Landau-Lifshitz方程组的局部解可以延拓到时刻T,从而得到了其强解的整体存在性.

When the given ‖∇u_(0)‖L^(2)+‖Δd_(0)‖L^(2) is properly small allowing large fluctuation of density,it is proved that the local solution of the three-dimensional variable density incompressible Navier-Stokes-Landau-Lifstz equations can be extended beyond the time T by using the energy method.Moreover,we obtain the global existence of its strong solution.