带阻尼项的2D Navier-Stokes方程的指数吸引子

摘要

研究2D Navier-Stokes方程在含有阻尼项时指数吸引子的存在性.讨论了当阻尼项c|u|βu在β≥0和1/3≤β≤2时,方程分别存在弱解和强解,进一步验证了解半群在空间V中存在有界吸收集以及满足条件C,从而得到了带阻尼项的2D Navier - Stokes方程的指数吸引子.%The existence of exponential attractor for the 2D Navier - Stokes equation with damping term is studied. In this paper we discuss the existence of weak solutions and strong solutions for the damping term c | u β u at β≥0 and 1/3≤β≤2 respectively and further proves the existence of bounded absorbing set and satisfying condition C of solution semigroups, thus obtains the exponential attractor of the 2D Navier - Stokes equation with damping term.