二维Navier-Stokes方程组的H^1一致吸引子

H^1-uniform Attractor for 2D Navier-Stokes Equations

该文讨论一类非自治Navier-Stokes方程组在二维区域(有界或无界)上一致吸引子的存在性与解的渐近光滑效应.作者应用拟能方程得到Navier-Stokes方程组生成的一簇过程的渐近紧性,并证明H^1一致吸引子的存在性.之后,作者证明了L^2一致吸引子属于H^1一致吸引子,从而在"解最终变得比初值光滑"的意义下揭示了Nayier-Stokes方程组解的渐近光滑效应.

This paper is concerned with the existence of uniform attractor and asymptotic smoothing effect of solutions for two-dimensional （2D） nonautonomous Navier-Stokes equa- tions in 2D domains （bounded or not）. The author uses the enstrophy equation to obtain the asymptotic compactness of the family of processes associated with the Navier-Stokes equations and establishes the existence of Hi-uniform attractor and thus reveal the asymptotic smoothing effect of the solutions in the sense that the solutions become eventually more regular than the initial data.