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- W2016648282 abstract "We perform a mathematical analysis of the steady flow of a viscous liquid, $${mathcal{L}}$$ , past a three-dimensional elastic body, $${mathcal{B}}$$ . We assume that $${mathcal{L}}$$ fills the whole space exterior to $${mathcal{B}}$$ , and that its motion is governed by the Navier–Stokes equations corresponding to non-zero velocity at infinity, v ∞. As for $${mathcal{B}}$$ , we suppose that it is a St. Venant–Kirchhoff material, held in equilibrium either by keeping an interior portion of it attached to a rigid body or by means of appropriate control body force and surface traction. We treat the problem as a coupled steady state fluid-structure problem with the surface of $${mathcal{B}}$$ as a free boundary. Our main goal is to show existence and uniqueness for the coupled system liquid-body, for sufficiently small |v ∞|. This goal is reached by a fixed point approach based upon a suitable reformulation of the Navier–Stokes equation in the reference configuration, along with appropriate a priori estimates of solutions to the corresponding Oseen linearization and to the elasticity equations." @default.
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- W2016648282 date "2009-03-28" @default.
- W2016648282 modified "2023-09-27" @default.
- W2016648282 title "Steady Flow of a Navier–Stokes Liquid Past an Elastic Body" @default.
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- W2016648282 doi "https://doi.org/10.1007/s00205-009-0224-y" @default.
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