On a Class of Energy Preserving Boundary Conditions for Incompressible Newtonian Flows

Source abstract

We derive a class of energy preserving boundary conditions for incompressible Newtonian flows and prove local-in-time well-posedness of the resulting initial boundary value problems, i.e., the Navier--Stokes equations complemented by one of the derived boundary conditions, in an $L_p$-setting in domains $\Omega \subseteq {\mathbb R}^n$, which are either bounded or unbounded with almost flat boundary of class $C^{3-}$. The results are based on maximal regularity properties of the underlying linearizations, which are also established in the above setting.