论文标题
带有时间的Navier-Stokes方程式准周期外力：准周期解决方案的存在和稳定性
The Navier-Stokes equation with time quasi-periodic external force: existence and stability of quasi-periodic solutions
论文作者
论文摘要
我们证明了对于不可压缩的Navier-Stokes方程式的小幅度，时间 - 周期性解决方案（不变的tori），$ d $ d $ d $二维的torus $ \ t^d $，带有时间外部力量的小，准周期性。我们还表明，它们在$ H^s $中是轨道和渐近稳定的（对于$ S $足够大）。更确切地说，对于任何靠近不变圆环的初始基准，都存在一个独特的全局时间解决方案，该解决方案始终保持靠近不变的圆环。此外，该解决方案以$ t \ to + \ infty $渐近地收敛到不变的圆环，并以任何任意$α\ in（0，1）$的融合率$ O（e^{ - αt}）$指数率。
We prove the existence of small amplitude, time-quasi-periodic solutions (invariant tori) for the incompressible Navier-Stokes equation on the $d$-dimensional torus $\T^d$, with a small, quasi-periodic in time external force. We also show that they are orbitally and asymptotically stable in $H^s$ (for $s$ large enough). More precisely, for any initial datum which is close to the invariant torus, there exists a unique global in time solution which stays close to the invariant torus for all times. Moreover, the solution converges asymptotically to the invariant torus for $t \to + \infty$, with an exponential rate of convergence $O( e^{- αt })$ for any arbitrary $α\in (0, 1)$.
