Existence Of Strong Solutions For A Class Of Fluid-Solid Coupling Systems

In this paper,we discuss the existence of strong solutions a class of fluid-structure interaction systems with multiple rigid bodies and incompressible fluids whose viscosity coefficients depend on densityWe first use the variable substitution to establish a nonlinear differential equation corresponding to the research object in this article.Then,the smooth solution of the linearization problem is obtained using the Garlerkin approxima-tion method,so that an approximate solution to the original problem can be constructed.By estimating the uniform boundedness of the approximated solu-tion,the existence of strong solutions for a class of coupled systems describing the motion of multiple rigid bodies in incompressible fluid is proved finally.In particular,this conclusion allows a vacuum to appear inside the fluid when the initial density meets the compatibility conditions.The chapters are arranged as follows:The first chapter of the introduction mainly describes the research signifi-cance of fluid-structure coupling problems and the research progress of domestic and foreign researchers on such problems.The rigid body is regarded as a fluid with sufficient viscosity,and the fluid-solid boundary is treated with the idea of??variable substitution,so as to establish a mathematical model of the entire fluid-solid coupling system from local to the wholeThe second chapter of the preliminaries mainly introduces the main assump-tions required in this article,as well as the inequality and related lemmas used in the proof processThe third chapter is the main part of the thesis.First,the smooth solution of the linearized problem is obtained by using the Garlerkin approximation method,thereby constructing the approximate solution of the original problem,and then obtaining the uniform boundedness of the approximate solution.Finally,the existence of strong solutions for this type of coupled system is proved,and a blasting criterion is given.