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arXiv · 2006.15663

Inertial manifolds via spatial averaging revisited

Anna Kostianko·Xinhua Li·Chunyou Sun·Sergey Zelik
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Abstract

The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. Mallet-Paret. We present a universal approach which covers the most part of known results obtained via this method as well as gives a number of new ones. Among our applications are reaction-diffusion equations, various types of generalized Cahn-Hilliard equations, including fractional and 6th order Cahn-Hilliard equations and several classes of modified Navier-Stokes equations including the Leray-$α$ regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.

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Anna Kostianko, Xinhua Li, Chunyou Sun, Sergey Zelik. 2020-06-28. Inertial manifolds via spatial averaging revisited. https://arxiv.org/abs/2006.15663

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