Existence Of Global Weak Solutions For Boussinesq Fluid-structure Coupling Systems With High Frequency Small Displacement Oscillations

In this thesis,we study the existence of global weak solutions for a class of fourth-order nonlinear hyperbolic equations and incompressible Boussinesq equations.Some achievements have been made on the fluid-structure coupling problem,and this thesis mainly establishes a three-dimensional fluid-structure coupling system for research,and the fluid-structure coupling problem and uniqueness problem of mobile interface are complex,so this thesis studies the static interface coupling problem of elastic insulation material under ideal state.This thesis is divided into three chapters.The first chapter mainly introduces the research background,significance and research status of fluid-structure coupling system.At the same time,the thesis also introduces the research content,symbol description and physical significance.The important applications of fluid-structure coupling system in many fields such as physics,engineering and biology are stated,and the great value of fluid mechanics is revealed.The second chapter describes the main research results of this,thesis and provides the preparatory knowledge required for this thesis,such as listing the main methods involved,inequalities and related theorems lemma.In this chapter,the definition of weak solution is given,and the original fluid-structure coupling system is transformed into weak equation.In chapter three,the existence of global weak solution for Boussinesq fluid-structure coupling system with high frequency small displacement oscillation is studied.In the first step,Galerkin method is applied to solve the finite dimensional approximate solution to construct the weak solution,and a set of ordinary differential equations is obtained.According to the existence and uniqueness theorem,the unique solution of the ordinary differential equations can be obtained.The second step is to estimate the energy of the approximate solution by using the two important lemmas and the uniform elliptic condition of the equation.The last step,the existence of weak solution is proved by compactness method,Aubin-Lions lemma,Holder inequality and other important inequalities.