in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of timedependent NavierStokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system c...

Abstract In this paper, in a cylindrical domain $D=\Omega \times (0,T)$ D = Ω × ( 0 , T ) with $\Omega \subset {R}^{n}$ ⊂ R <mml:...

In this paper we investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness/ellipticity on the coefficient function and very mild conditions on the geometry of the domain – including a very weak compatibility condition between the Dirichlet boundary part and its complement – we prove Hölder continuity of the solu...