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arXiv · 2607.23756

Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data

Mario Bukal·Igor Kukavica·Linfeng Li·Boris Muha
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Abstract

We consider a three-dimensional fluid-structure interaction problem coupling the incompressible Navier-Stokes equations in a time-dependent domain with a square-root damped plate equation, which is posed on the moving upper boundary of the fluid. We prove, a priori, the exponential decay of strong solutions for initial data that are sufficiently small in a suitable Sobolev space. The proof combines higher-order energy estimates, Stokes-type regularity bounds, and a nonlinear bootstrap scheme that closes under the smallness assumption.

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Mario Bukal, Igor Kukavica, Linfeng Li, Boris Muha. 2026-07-26. Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data. https://arxiv.org/abs/2607.23756

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