Navier-Stokes equations interacting with a nonlinear elastic fluid shell

Details Navier-Stokes equations interacting with a nonlinear elastic fluid shell Navier-Stokes equations interacting with a nonlinear elastic fluid shell

2006-04-13

arxiv.org/abs/math/0604313v2

Mathematics

Analysis of PDEs

56 pages, 1 figure

Scientific paper

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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