# American Institute of Mathematical Sciences

July  2016, 21(5): 1455-1468. doi: 10.3934/dcdsb.2016006

## Free boundary problems for systems of Stokes equations

 1 The Ohio State University, Department of Mathematics, Columbus, OH 43210, United States

Received  May 2015 Revised  November 2015 Published  April 2016

Recent years have seen a dramatic increase in the number and variety of new mathematical models describing biological processes. Some of these models are formulated as free boundary problems for systems of PDEs. Relevant biological questions give rise to interesting mathematical questions regarding properties of the solutions. In this review we focus on models whose formulation includes Stokes equations. They arise in describing the evolution of tumors, both at the macroscopic and molecular levels, in wound healing of cutaneous wounds, and in biofilms. We state recent results and formulate some open problems.
Citation: Avner Friedman. Free boundary problems for systems of Stokes equations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1455-1468. doi: 10.3934/dcdsb.2016006
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