【摘要】 该文研究具有非线性阻尼的非自治Navier-Stokes-Voigt方程的长时间动力学.首先,利用Galerkin方法证明了整体弱解的存在唯一性.然后,利用能量方法建立解过程的一致渐近紧性,从而证明了拉回吸引子的存在性.此外,还建立了固定有界集族上的吸引子与满足缓增条件的集族上的吸引子之间的关系.更多还原

【Abstract】 In this paper,we are concerned with the long-time behavior of solutions to the non-autonomous Navier-Stokes-Voigt equations with nonlinear damping.Firstly,we prove the existence and uniqueness of global weak solutions by the Galerkin method.Then,we focus on studying the existence of pullback attractors by using an energy method,which is more simple than the weak continuous method to establish the uniformly asymptotical compactness.In addition,some relationships between the attractors for the universe of fixed bounded sets and those associated to a universe given by another tempered condition are established.更多还原