BibTeX
@MISC{Franzke_strongsolutions,
author = {Martin Franzke},
title = {Strong Solutions of the Navier-Stokes Equations in Aperture Domains},
year = {}
}
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Abstract
We consider the nonstationary Navier-Stokes equations in an aperture domain R 3 consisting of two halfspaces separated by a wall, but connected by a hole in this wall. In this special domain one has to impose an auxiliary condition to single out a unique solution. This can be done by prescribing either the ux through the hole or the pressure drop between the two halfspaces. We construct suitable Stokes operators for both of the auxiliary conditions and show that they generate holomorphic semigroups. Then we prove the existence and uniqueness of solutions as well as a maximal regularity estimate for the Stokes equations subject to one of the auxiliary conditions. For the corresponding Navier-Stokes equations we prove existence and uniqueness of local in time solutions. 1 Introduction The ow of a viscous incompressible uid in a region with rigid walls is governed by the following Navier-Stokes equations: u t u + uru +rp = f in (0; T ); u(0) = u 0 in ; div u = 0 in...
Keyphrases
aperture domain navier-stokes equation auxiliary condition strong solution nonstationary navier-stokes equation rigid wall corresponding navier-stokes equation special domain one uru rp viscous incompressible uid time solution holomorphic semigroups pressure drop unique solution stokes equation following navier-stokes equation suitable stokes operator maximal regularity estimate
