1307.3496 (P. Kalita et al.)

Attractors for Navier-Stokes flows with multivalued and nonmonotone
subdifferential boundary conditions    [PDF]

P. Kalita, G. Łukaszewicz

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.

View original: http://arxiv.org/abs/1307.3496