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Regularity of solutions to the Stokes equations under a certain nonlinear boundary condition. (English) Zbl 0995.35048
Salvi, Rodolfo (ed.), The Navier-Stokes equations: theory and numerical methods. Proceedings of the international conference, Varenna, Lecco, Italy, 2000. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 223, 73-86 (2002).
Summary: The regularity of a solution to the variational inequality for the Stokes equation is considered. The inequality describes the steady motion of the viscous incompressible fluid under a certain unilateral constraint of friction type. Firstly the solution is approximated by solutions to a regularized problem which is introduced by Yosida’s regularization for a multivalued operator. Then we establish a regularity result to the regularized problem. The regularity of the solution to the original inequality follows by the limiting argument.
For the entire collection see [Zbl 0972.00046].

MSC:
35Q30 Navier-Stokes equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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