Weak solutions to the generalized Navier–Stokes equations with mixed boundary conditions and implicit obstacle constraints
- Authors: Cen J.; Nguyen V.T.; Vetro C.; Zeng S.
- Publication year: 2023
- Type: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/618026
Abstract
This paper is concerned with the investigation of a generalized Navier-Stokes equation for non-Newtonian fluids of Bingham-type (GNSE, for short) involving a multivalued and nonmonotone slip boundary condition formulated by the generalized Clarke subdifferential of a locally Lipschitz superpotential, a no leak boundary condition, and an implicit obstacle inequality. We obtain the weak formulation of (GNSE) which is a generalized quasi-variational-hemivariational inequality. By introducing an Oseen model as an auxiliary (intermediated) problem and employing Kakutani-Ky Fan theorem for multivalued operators as well as the theory of nonsmooth analysis, an existence theorem to (GNSE) is established.