We study the stationary two-dimensional incompressible flow of non-Newtonian fluid governed by a nonlinear constitutive law and with a multivalued nonmonotone subdifferential frictional boundary condition. We provide an abstract result on existence of solution to an operator inclusion modeling the flow phenomenon. We prove a theorem on existence and, under additional assumptions, also uniqueness of weak solution to the flow problem.Mathematics Subject Classification. 76D05 · 47J20 · 49J40 · 35Q30.

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. K E Y W O R D Sfrictional type boundary condition, generalized Newtonian fluid, leak, operator inclusion, Oseen model, slip, unilateral boundary condition 2 0 1 0 M A In this paper we introduce and analyse a new class of operator inclusions of subdifferential type and a corresponding class of elliptic variational-hemivariational inequalities in a reflexive Banach space. Our main goal is to provide existence results to these classes of problems, and apply them to examine the stationary flow Oseen model of generalized Newtonian fluid described by equations − Div + ( ⋅ ∇) + ∇ = in Ω, div = 0 in Ω

No abstract

No abstract

We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter 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. The weak form of the problem leads to a new class of variational–hemivariational inequalities on convex sets for the velocity field. Solution existence and the weak compactness of the solution set to the inequality problem are established based on the Schauder fixed point theorem.