Gevrey Regularity for a Fluid-Structure Interaction Model

2024/08/21 by George Avalos, Avalos, George, Dylan McKnight +3 · 2 citations
Earth and Planetary Sciences · Mathematics · #35B65 #35Q35 #35Q74 #74F10 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2408.12000

openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A result of Gevrey regularity is ascertained for a semigroup which models a fluid-structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry O. On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the conclusion of Gevrey regularity is an appropriate estimation of the resolvent of the associated C₀-semigroup operator. Moreover, a numerical scheme and example is provided which empirically demonstrates smoothing of the fluid-structure semigroup.

Cited by

• Analysis and Numerical Approximation to Interactive Dynamics of Navier Stokes-Plate Interaction PDE System
• Local well-posedness of the initial value problem in Einstein-Cartan theory

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