Global attractors in stronger norms for a class of parabolic systems with nonlinear boundary conditions

2012/02/17 by Martin Meyries, Meyries, Martin
Engineering · Mathematics · #Navier-Stokes equation solutions #Numerical methods in inverse problems #Stability and Controllability of Differential Equations #math.AP #msc:35B41 #msc:35K60

paper · pdf · doi:10.48550/arxiv.1202.3867

This is a preprint version. Published in Nonlinear Analysis 75 (2012) 2922-2935

arxiv created 2012/02/17 · arxiv updated 2012/02/20

Abstract

For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are sufficient for the existence of a global attractor in this phase space. The approach relies on maximal L_p-regularity with temporal weights for the linearized problem. An inherent smoothing effect due to the weights is employed for gradient estimates. In several applications we can improve the convergence to an attractor by one regularity level.

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