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arXiv · 1909.09344

$L^p$-theory for a fluid-structure interaction model

Robert Denk·Jürgen Saal
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Abstract

We consider a fluid-structure interaction model for an incompressible fluid where the elastic response of the free boundary is given by a damped Kirchhoff plate model. Utilizing the Newton polygon approach, we first prove maximal regularity in $L^p$-Sobolev spaces for a linearized version. Based on this, we show existence and uniqueness of the strong solution of the nonlinear system for small data.

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Robert Denk, Jürgen Saal. 2019-09-20. $L^p$-theory for a fluid-structure interaction model. https://doi.org/10.1007/s00033-020-01387-5

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