修正的Navier-Stokes方程的周期轨道及渐近稳定性

Periodic Orbit and Asymptotic Stabilityof the Modified NavierStokes Equations

考虑由修正的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程产生的动力系统｛Ｖｔ，ｔ∈Ｒ，Ａ｝，Ａ是Ｈ中有界不变集．利用Ｓｅｌ定理证明了在ｆ，１／α２，１／α３小的条件下，ａ∈Ａ，其ω－极限集ω（ａ）是一周期运动，而且此周期运动是渐近稳定的．

 Under the condition that f,1/α2,1/α3 are small enough for the modified NavierStokes equations,we prove that ωlimit set ω(a) consists of single periodic orbit,and the periodic motion is asymptotic stability for any point a∈A,,where A is bounded invariant set.Our proof is based on Sell′s theorem.