Anna Kostianko, Xinhua Li, Chunyou Sun, Sergey Zelik
Published 2020-06-28Version 1
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-$\alpha$ regularization, hyperviscous regularization and their combinations. All of the results are obtained in 3D case with periodic boundary conditions.
Inertial manifolds for the 3D modified-Leray-$α$ model with periodic boundary conditions
Inertial manifolds for 1D reaction-diffusion-advection systems. Part II: periodic boundary conditions
Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions
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