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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 495408, 9 pages
Research Article

Classical Solvability of a Free Boundary Problem for an Incompressible Viscous Fluid with a Surface Density Equation

Department of Mathematics, Faculty of Engineering, Tamagawa University, 6-1-1 Tamagawa-Gakuen, Machida, Tokyo 194-8610, Japan

Received 16 June 2013; Accepted 8 August 2013

Academic Editor: Rodrigo Lopez Pouso

Copyright © 2013 Yoshiaki Kusaka. 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.


We investigate a mathematical model introduced by Shikhmurzaev to remove singularities that arise when classical hydrodynamic models are applied to certain physical phenomena. The model is described as a free boundary problem consisting of the Navier-Stokes equations and a surface mass balance equation. We prove the local-in-time solvability in Hölder spaces.