Navier-Stokes equations interacting with a nonlinear elastic fluid shell

2006/04/13 by C. H. Arthur Cheng, Cheng, C. H. Arthur, Daniel Coutand +3
Computer Science · Engineering · Mathematics · #35Q30 #74F10 #74K25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.math/0604313

openalex publication_date 2006/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic fluid shell. The fluid motion is governed by the Navier-Stokes equations, while the fluid shell is modeled by a bending energy which extremizes the Willmore functional and a membrane energy that extremizes the surface area of the shell. The fluid flow and shell deformation are coupled together by continuity of displacements and tractions (stresses) along the moving material interface. We prove existence and uniqueness of solutions in Sobolev spaces.

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