2020/06/28 by Kostianko, Anna, Li, Xinhua, Sun, Chunyou +1 · 1 citation
#35B33 #35B40 #35B42 #35Q30 #76F20 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2006.15663
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.