带阻尼项的非自治2D Navier-Stokes方程的一致吸引子

摘要

考虑带阻尼项cu βu的非自治2DNavier-Stokes方程解的长时间动力学行为,应用一些新结果和能量估计技巧,获得了能量的一致衰退估计。结果表明,当外力项满足正规条件(而非平移紧),阻尼项参数c>0,1/3≤β≤2,初值uτ∈cl(H10(Ω))2{u∈C∞0(Ω)2, divu=0}时,阻尼型非自治2DNavier-Stokes方程满足一致(C)条件,从而证明了一致吸引子在cl(H10(Ω))2{u∈C∞0(Ω)2, divu=0}内的存在性。%The long-time dynamic behavior of the solutions for the non-autonomous 2D Navier-Stokes equations with weak damping term cu βu was discussed.Based on some new results and techniques of energy estimates,the uniformly decay estimate was obtained.When the forcing term only satisfies the normal condition instead of translation compact,the parameters of damping term c >0,1/3 ≤β≤2 , and initial data uτ∈ cl(H 10 (Ω))2 {u ∈ C ∞0 (Ω)2 ,div u = 0 },for the non-autonomous 2D Navier-Stokes equations with weak damping term,uniform condition (C)was verified and the existence of uniform attractors in cl(H10 (Ω))2 {u∈C ∞0 (Ω)2 ,div u=0}was shown.