Regular solutions of a problem coupling a compressible fluid and an elastic structure. (English) Zbl 1426.76651
Summary: We are interested in 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 modeled 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 linearized problem 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.
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 linearized problem 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.
MSC:
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 35Q30 | Navier-Stokes equations |
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