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arXiv · 2308.04253

Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations

Sebastian Schwarzacher·Pei Su
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Abstract

A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The coupling is partially of geometric nature, as the geometry of the fluid domain is changing in accordance to the motion of the beam. Here the existence of a unique strong solution for large initial data and all times up to geometric degeneracy is shown. For that an a-priori estimate on the time-derivative of the coupled solution is introduced. For the Navier-Stokes part it is a borderline estimate in the spirit of Ladyzhenskaya applied directly to the in-time differentiated system.

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Sebastian Schwarzacher, Pei Su. 2023-08-08. Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations. https://arxiv.org/abs/2308.04253

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