Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions
Analysis of PDEs
2015-09-28 v2 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered problem which is governed by a partial differential inclusion with a multivalued term in the form of Clarke subdifferential. Then we prove the existence of a trajectory attractor and a weak global attractor for the associated multivalued semiflow. This research is motivated by control problems for fluid flows in domains with semipermeable walls and membranes.
Keywords
Cite
@article{arxiv.1307.3496,
title = {Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions},
author = {P. Kalita and G. Łukaszewicz},
journal= {arXiv preprint arXiv:1307.3496},
year = {2015}
}
Comments
A correction was introduced in assertion (ii) of Definition 4.4 and - accordingly - in the proof of Theorem 4.3