Improved boundary regularity for a Stokes-Lam 'e system

2020/09/10 by Francesca Bucci, Bucci, Francesca
Engineering · Mathematics · #35B65 #35M33 #35Q74 #35Q93 #49N10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.04905

openalex created_date 2019/11/22 · openalex publication_date 2020/09/10 · openalex updated_date 2026/07/28

Abstract

This paper recalls a partial differential equations system, which is the\nlinearization of a recognized fluid-elasticity interaction three-dimensional\nmodel. A collection of regularity results for the traces of the fluid variable\non the interface between the body and the fluid is established, in the case a\nsuitable boundary dissipation is present. These regularity estimates -- in time\nand space, of local and global nature -- are geared toward ensuring the\nwell-posedness of the algebraic Riccati equations which arise from the\nassociated optimal boundary control problems on an infinite time horizon. The\ntheory of operator semigroups and interpolation provide the main tools.\n

Related

• Regularity of boundary traces for a fluid-solid interaction model
• Optimal boundary control with critical penalization for a PDE model of fluid-solid interactions
• Partial boundary regularity for the Navier-Stokes equations in time-dependent domains
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• Optimal regularity results for the Stokes--Dirichlet problem