| Abstract: |
| Inertial manifold (IM) is a finite-dimensional invariant manifold that contains the global attractor and that attracts all the orbits at an exponential rate, and it is also a graph of some Lipschitz continuous functions. If a PDE possesses an IM, then its dynamical can be completely determined by a system of ODEs. Classical theory of IM required a so-called spectral gap condition for constructing an IM. In this talk, we introduce the method of spatial averaging which can construct IMs without spectral gap condition and consider the application for 2D modified Navier-Stokes equations (NSEs). An original motivation for the theory of IMs was treating the NSEs. Unfortunately, this problem is still open now. This talk will review key results concerning IMs for modified NSEs and present our recent contributions to this topic. |
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