Global strong solutions of two-dimensional Navier–Stokes equations with nonlinear slip boundary conditions

Abstract

The two-dimensional time-dependent Navier–Stokes equations with nonlinear slip boundary conditions are investigated in this paper. Since the nonlinear slip boundary conditions of this type include the subdifferential property, the weak variational formulation is the variational inequality. The existence, uniqueness and regularity of global weak solutions are shown using the regularized method. Moreover, the continuous dependence property of the weak solution for given initial data and the behavior of the global weak solution as t⟶+∞ are established.