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arXiv · 1307.3496

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

P. Kalita·G. Łukaszewicz
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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.

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P. Kalita, G. Łukaszewicz. 2013-07-12. Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions. https://doi.org/10.1016/j.nonrwa.2014.03.002

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