Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction

  title={Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction},
  author={Jeffrey Kuan and Tadahiro Oh and Sun{\vc}ica {\vC}ani{\'c}},
  journal={Applicable Analysis},
  pages={4349 - 4373}
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid–structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on (rough) data, often arising in real-life problems, for which it is known that the deterministic problem is ill-posed. We show that random perturbations of such data give rise almost surely to the existence of a unique solution. More specifically, we prove… 
2 Citations

Figures from this paper

On the two-dimensional singular stochastic viscous nonlinear wave equations

. We study the stochastic viscous nonlinear wave equations (SvNLW) on T 2 , forced by a fractional derivative of the space-time white noise ξ . In particular, we consider SvNLW with the singular

Introduction to the Andro Mikelic memorial volume

aCentre de Mathématiques Appliquées, École Polytechnique, CNRS, Institut Polytechnique de Paris, Palaiseau, France; bBâtiment IPRA, Université de Pau et des Pays de l’Adour, Pau, France; cDepartment



A stochastically perturbed fluid-structure interaction problem modeled by a stochastic viscous wave equation

Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction

We study low regularity behavior of the nonlinear wave equation in $\mathbb{R}^2$ augmented by the viscous dissipative effects described by the Dirichlet-Neumann operator. Problems of this type arise

Generation of bounded semigroups in nonlinear subsonic flow–structure interactions with boundary dissipation

We consider a subsonic flow–structure interaction describing the flow of gas above a flexible plate. A perturbed wave equation describes the flow, and a second‐order nonlinear plate equation

A nonlinear, 3D fluid-structure interaction problem driven by the time-dependent dynamic pressure data: a constructive existence proof

This work proves the existence of a weak solution to this 3D FSI problem by using an operator splitting approach in combination with the Arbitrary Lagrangian Eulerian mapping, which satisfies a geometric conservation law property.

Existence of Global Strong Solutions to a Beam–Fluid Interaction System

We study an unsteady nonlinear fluid–structure interaction problem which is a simplified model to describe blood flow through viscoelastic arteries. We consider a Newtonian incompressible

Smoothness of weak solutions to a nonlinear fluid-structure interaction model

The nonlinear fluid-structure interaction coupling the Navier-Stokes equations with a dynamic system of elasticity is consid- ered. The coupling takes place on the boundary (interface) via the con-

Existence of a weak solution to a nonlinear fluid-structure interaction problem modeling the flow of an incompressible , viscous fluid in a cylinder with deformable walls

We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by

The Interaction between Quasilinear Elastodynamics and the Navier-Stokes Equations

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