In this paper, for the Navier-Stokes equations in a bounded connected polygon or polyhedron \(\Omega \subset R^d\), \(d=2,3\), with a homogenous stress type mixed boundary condition, we establish an a priori estimate for the weak solutions and the existence result without small data and/or large viscosity restriction. And a global uniqueness result is obvious based on the a priori estimate obtained.
Navier-Stokes equations Mixed boundary conditions A priori estimate Existence Global uniqueness
This is a preview of subscription content, log in to check access.
Bernardi, C., Hecht, F., Verfürth, R.: A finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. ESAIM: Math. Model. Numer. Anal. 43, 1185–1201 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
Maz’ya, V., Rossmann, J.: Mixed boundary value problems for the stationary Navier-Stokes system in polyhedral domains. Arch. Rational Mech. Anal 194, 669–712 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
Castillo, P., Cockburn, B., Perugia, I., Schötzau, D.: An a priori error analysis of the local discontinuous Galerkin method for elliptic problems. SIAM J. Numer. Anal. 38(5), 1676–1706 (2000)MathSciNetCrossRefzbMATHGoogle Scholar