On the interaction between quasilinear elastodynamics and the Navier-Stokes equations
Skip to main content
eScholarship
Open Access Publications from the University of California

On the interaction between quasilinear elastodynamics and the Navier-Stokes equations

  • Author(s): Coutand, Daniel
  • Shkoller, Steve
  • et al.

Published Web Location

https://arxiv.org/pdf/math/0503431.pdf
No data is associated with this publication.
Abstract

The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible Navier-Stokes equations along a moving interface. Unlike our approach for the case of linear elastodynamics, we cannot employ a fixed-point argument on the nonlinear system itself, and are instead forced to regularize it by a particular parabolic artificial viscosity term. We proceed to show that with this specific regularization, we obtain a time interval of existence which is independent of the artificial viscosity; together with a priori estimates, we identify the global solution (in both phases), as well as the interface motion, as a weak limit in srong norms of our sequence of regularized problems.

Item not freely available? Link broken?
Report a problem accessing this item