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A new class of variational‐hemivariational inequalities for steady Oseen flow with unilateral and frictional type boundary conditions
Author(s) -
Migórski Stanisław,
Dudek Sylwia
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900112
Subject(s) - mathematics , boundary value problem , mathematical analysis , subderivative , weak solution , slip (aerodynamics) , nonlinear system , variational inequality , banach space , type (biology) , geometry , physics , regular polygon , ecology , convex optimization , quantum mechanics , biology , thermodynamics
We study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady Oseen model for a generalized Newtonian incompressible fluid. A variational‐hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier‐Fujita slip condition, and the threshold slip and leak condition of frictional type.