Existence results for regularized equations of second-grade fluids with wall slip

Abstract

In this paper, we study the equations governing the steady motion of a class of second-grade fluids in a bounded domain of $\mathbb{R}^n$, ${n=2,3}$, with the nonlinear slip boundary condition. We prove the existence of a weak solution without assuming smallness of the data. Moreover, we give estimates for weak solutions and show that the solution set is sequentially weakly closed.

Keywords

• nonlinear pde
• existence theorem
• operator theory
• weak solutions
• second-grade fluids
• slip boundary conditions