Table of Contents
ISRN Mathematical Physics
Volume 2012 (2012), Article ID 407940, 19 pages
http://dx.doi.org/10.5402/2012/407940
Research Article

On Strong Solutions of Regularized Model of a Viscoelastic Medium with Variable Boundary

Department of Mathematics, Voronezh State University, Universitetskaya pl., 1, Voronezh 394 000, Russia

Received 29 September 2011; Accepted 19 October 2011

Academic Editor: Y. Xu

Copyright © 2012 Vladimir Orlov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the initial-value problem for systems of equations describing the evolution of a viscoelastic medium with variable boundary with memory along the trajectories of a velocity field, which generalizes the Navier-Stokes system of equations. Nonlocal existence and uniqueness theorem of strong solutions containing senior square-integrable derivatives in the planar case are established.