Navier-Stokes equations interacting with a nonlinear elastic solid shell

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

2006-11-22

arxiv.org/abs/math/0611670v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by the nonlinear Koiter shell model, consisting of both bending and membrane tractions. The fluid is coupled to the solid shell through 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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