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Regular solutions of a problem coupling a compressible fluid and an elastic structure

Muriel Boulakia 1, 2 Sergio Guerrero 1
2 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : We are interested by the three-dimensional coupling between a compressible viscous fluid and an elastic structure immersed inside the fluid. They are contained in a fixed bounded set. The fluid motion is modelled by the compressible Navier-Stokes equations and the structure motion is described by the linearized elasticity equation. We establish the local in time existence and the uniqueness of regular solutions for this model. We emphasize that the equations do not contain extra regularizing term. The result is proved by first introducing a problem linearized and by proving that it admits a unique regular solution. The regularity is obtained thanks to successive estimates on the unknowns and their derivatives in time and thanks to elliptic estimates. At last, a fixed point theorem allows to prove the existence and uniqueness of regular solution of the nonlinear problem.
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Muriel Boulakia, Sergio Guerrero. Regular solutions of a problem coupling a compressible fluid and an elastic structure. Journal de Mathématiques Pures et Appliquées, Elsevier, 2010, 94 (4), pp.341-365. ⟨10.1016/j.matpur.2010.04.002⟩. ⟨hal-00648710⟩

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