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Existence for an unsteady fluid-structure interaction problem. (English) Zbl 0969.76017
The paper deals with fluid-structure interaction in the case where the fluid is time-dependent and the structure is a collection of rigid bodies. The authors consider two- and three-dimensional viscous incompressible flows satisfying the Navier-Stokes equations. The fluid domain depends on time and is defined by the position of the structure, itself resulting from a stress distribution coming from the fluid. The whole problem is nonlinear, and the equations are coupled. The authors prove local solvability in time. The proof is based on the estimates of nonlinear terms and on the Banach fixed point theorem (contraction mapping principle). This result is an interesting contribution to generalized problems for Navier-Stokes equations, which uses classical techniques carefully adapted to new situation.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
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