A free boundary inviscid model of flow-structure interaction

2022/05/24 by Kukavica, Igor, Tuffaha, Amjad · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.12103

Abstract

We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a~priori estimates for the existence with the optimal regularity H^r, for r>2.5, on the fluid initial data and construct a unique solution of the system for initial data u₀∈ H^r for r≥3. An important feature of the existence theorem is that the Taylor-Rayleigh instability does not occur.

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• A geophysical free-boundary system modeling an ice-sheet interacting with an ocean
• Strong stability and the Schiffer Conjecture for the fluid-elastic semigroup
• The Euler equations with variable coefficients

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