Navier-Stokes equations interacting with a nonlinear elastic biofluid shell

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 with density given by a convex function of the local area ratio. The fluid flow and shell deformation are coupled together by continuity of displacements and tractions (stresses) along the moving surface defining the shell. We prove the existence and uniqueness of solutions in Sobolev spaces for a short time.