Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow. (English) Zbl 1354.35099
Summary: A time-dependent Stokes fluid flow problem is studied with nonlinear boundary conditions described by the Clarke subdifferential. We present equivalent weak formulations of the problem, one of them in the form of a hemivariational inequality. The existence of a solution is shown through a limiting procedure based on temporally semi-discrete approximations. Uniqueness of the solution and its continuous dependence on data are also established. Finally, we present a result on the existence of a solution to an optimal control problem for the hemivariational inequality.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35A15 | Variational methods applied to PDEs |
| 35A35 | Theoretical approximation in context of PDEs |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 47J20 | Variational and other types of inequalities involving nonlinear operators (general) |
| 76D07 | Stokes and related (Oseen, etc.) flows |
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