| Abstract: |
| Consider a rigid body $S$ moving through a Navier-Stokes liquid $L$ which fills the three-dimensional domain exterior to it, and the steady state regime of the system $\{S,L\}$, as seen by an observer attached to the solid. Self-propulsion means that the total net force and torque, external to the system $\{S,L\}$, acting on $S$, are identically zero, and may be produced by drawing fluid inwards across portions of the boundary and expelling it from others, or by moving tangentially portions of the boundary. We will see that the problem of finding appropriate boundary values that generate a prescribed motion of $S$ can be solved as a control problem. We will also investigate how to minimize the work needed to overcome the drag exerted by the fluid on the solid. |
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