Von Karman plate in a gas flow: recent results and conjectures

TL;DR

This paper surveys recent mathematical research on flow-structure interactions involving a modified wave equation coupled with nonlinear elasticity, focusing on aeroelastic phenomena like flutter and divergence in subsonic and supersonic flows.

Contribution

It provides a comprehensive overview of recent advances in PDE analysis of flow-structure interactions, highlighting open problems and conjectures in aeroelasticity.

Findings

Analysis of well-posedness for coupled PDEs

Results on asymptotic stability and convergence

Discussion of conjectures based on experiments

Abstract

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation (PDE) treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well known observations and conjectures based on experimental/numerical studies.