EAN: 9783319927824

MATHEMATICAL THEORY OF EVOLUTIONARY FLUID-FLOW ...

This book is devoted to the study of coupled partial differential equation models  which
describe complex dynamical systems occurring in modern scientific applications such as fluid
flow-structure interactions. The first chapter provides a general description of a
fluid-structure interaction  which is formulated within a realistic framework  where the
structure subject to a frictional damping moves within the fluid. The second chapter then
offers a multifaceted description  with often surprising results  of the case of the static
interface  a case that is argued in the literature to be a good model for small  rapid
oscillations of the structure. The third chapter describes flow-structure interaction where the
compressible Navier-Stokes equations are replaced by the linearized Euler equation  while the
solid is taken as a nonlinear plate  which oscillates in the surrounding gas flow. The final
chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or
elasticity  as they arise in the context of high intensity ultrasound applications.

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