Weak Solvability of Equations Modeling Steady-State Flows of Second-Grade Fluids

Abstract

We prove the existence of continuous weak solutions of the nonlinear equations describing steady-state flows of second-grade fluids in a bounded three-dimensional domain under the no-slip boundary condition. A weak solution is found using the Galerkin method with special basis functions constructed with the help of a perturbed Stokes operator. An energy inequality for the resulting solution is derived.