On a Class of Energy Preserving Boundary Conditions for Incompressible   Newtonian Flows
  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 Lp-setting in domains, which are either bounded or unbounded with almost flat, sufficiently smooth boundary. The results are based on maximal regularity properties of the underlying linearisations, which are also established in the above setting. 
Dieter Bothe, Matthias K\"ohne, Jan Pr\"uss
math.AP