Some non‐standard problems in viscous flow
Lawrence Edward Payne, Philip W. Schaefer, Junqiang Song · Mathematical Methods in the Applied Sciences · 2004
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 © 2004 John Wiley & Sons, Ltd.