Global well-posedness of a nonlinear Boussinesq-fluid-structure interaction system with large initial data

TL;DR

This paper proves the global existence and uniqueness of solutions for a complex nonlinear fluid-structure interaction system involving heat exchange, using advanced mathematical techniques in two and three dimensions.

Contribution

It establishes the first comprehensive proof of well-posedness for a coupled Boussinesq-fluid-structure system with large initial data.

Findings

Existence of weak solutions in 2D and 3D

Uniqueness of weak solutions in 2D

Existence and uniqueness of strong solutions in 2D for large initial data

Abstract

In this paper, we consider the global well-posedness of the initial-boundary value problem to a nonlinear Boussinesq-fluid-structure interaction system, which describes the motion of an incompressible Boussinesq-fluid surrounded by an elastic structure with the heat exchange and is one coupled incompressible Boussinesq equations with the wave equation and heat equation by physical interface boundary conditions. Firstly, the global existence of weak solutions to this problem in two/three-dimension is proven by introducing one class of its suitable weak solution and using the compactness method. Then, the uniqueness of the weak solution to this problem in two-dimension is established. Finally, the existence and uniqueness of the global strong and smooth solution to this problem in two-dimension is obtained for any smooth large initial data under the assumptions of suitable compatibility conditions by establishing a priori higher order derivative estimates.