二维全平面上具阻尼的Nevier-Stokes方程的指数吸引子

Exponential Attractor of Nevier Stokes Equation with Damping On the Whole Plane

讨论二维全平面 Neiver- Stokes方程 tu -γ△ u +αu +u( .u) =f (x,t)∈Ω× R+ (1)div u =0 (2 )u(x,t)∈ H10 (Ω ) t>0 (3)u(x,0 ) =u0 (x)∈ H∩ H0 ,r (4 )其中Ω =R2 ,u =(u1,u2 )为速度场 ,f为外力 ,α >0 ,αu为与速度场平行的阻尼项 ,可理解为流体内部耗散的零阶近似 ,利用算子分解的方法 ,引入加权函数 ,我们证明问题 (1)～ (4 )在 H中存在指数吸引子 .

This paper studied the Nevier Stokes equation on the whole plane. tu-γ△u+αu+u(·u)=f (x,t)∈Ω×R +(1) div u=0(2) u(x,t)∈H 1 0(Ω) t>0(3) u(x,0)=u 0(x)∈H∩H 0,r (4)where Ω=R 2, u=(u 1,u 2) By using the method of operator decomposition and introducing weighted function, we prove the existence of exponential attractor for equation (1)～(4) in H space.