Some non-standard problems in viscous flow

Abstract

Energy bounds are derived for Dirichlet type boundary value problems for the Navier-Stokes and Stokes equations when a combination of the solution values initially and at a later time is prescribed. The bounds are obtained by means of a differential inequality and imply uniqueness and continuous data dependence of the solutions for a range of values of the parameter in the non-standard auxiliary condition. Copyright (C) 2004 John Wiley Sons, Ltd.