非自治Navier-Stokes方程的指数拉回吸引子

Exponential attractors for nonautonomous Navier-Stokes equations

近年来,非自治偏微分方程及其产生的过程引起了许多学者的关注.数学物理演化方程所产生的耗散动力系统的长时间动力行为可以用所谓的指数吸引子描述.在非自治情况下,有不同的方法寻找自治情况下的指数吸引子的对应物.拉回指数吸引子是作为描述非自治动力系统长期行为的一个适当的概念,它是具有有限分形维数的半不变的最小紧集族,拉回吸引相空间中的任意有界子集.证明了在有界域上的二维非自治Navier-Stokes方程在(H^(1)_(0)(Ω))^(2)中的拉回指数吸引子的存在性.

Recently,many authors have paid much attention to non-autonomous differential equations and the processes generated by them.It is well known that the long-time behavior of dissipative dyna mical systems generated by evolution equations of mathematical physics can be described in terms of the so-called exponential attractor.Different approaches were made to find the counterpart of the exponential attractors in the non-autonomous casei.Pullback exponential attractors,as a suitable notion describing long time behavior of non-autonomous dynamical systems,which is a minimal family of compact sets with finite fractal dimension semi-invariant under the process and pullback attracting each bounded subset of the phase space.In this paper,we prove the existence of pullback exponential attractors in(H^(1)_(0)(Ω))^(2) for a non-autonomous Navier-Stokes equation in a 2D bounded domainΩ.