C. Conca et al., Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, COMM PART D, 25(5-6), 2000, pp. 1019-1042
We introduce a concept of weak solution for a boundary value problem modell
ing the interactive motion of a coupled system consisting in a rigid body i
mmersed in a viscous fluid. The fluid, and the solid are contained in a fix
ed open bounded set of R-3. The motion of the fluid is governed by the inco
mpressible Navier-Stokes equations and the standard conservation's laws of
linear, and angular momentum rules the dynamics of the rigid body. The time
variation of the fluid's domain (due to the motion of the rigid body) is n
ot known apriori, so we deal with a free boundary value problem. Our main t
heorem asserts the existence of at least one weak solution for this problem
. The result is global in time provided that the rigid body does not touch
the boundary.