# American Institute of Mathematical Sciences

April  2013, 33(4): 1513-1544. doi: 10.3934/dcds.2013.33.1513

## Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid

 1 Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States

Received  October 2011 Revised  April 2012 Published  October 2012

Our goal in this paper is to investigate how the geometric shape of a swimmer affects the forces acting upon it in a 3-$D$ incompressible fluid, such as governed by the non-stationary Stokes or Navier-Stokes equations. Namely, we are interested in the following question: How will the swimmer's internal forces (i.e., not moving the center of swimmer's mass when it is not inside a fluid) transform'' their actions when the swimmer is placed into a fluid (thus, possibly, creating its self-propelling motion)?We focus on the case when the swimmer's body consists of either small parallelepipeds or balls. Such problems are of interest in biology and engineering application dealing with propulsion systems in fluids.
Citation: Alexander Khapalov, Giang Trinh. Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1513-1544. doi: 10.3934/dcds.2013.33.1513
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