一类流固耦合系统强解的存在性问题

本文主要讨论一类多刚体与粘性系数依赖于密度的不可压缩流体耦合系统的强解存在性问题.首先,利用变量替换建立本文研究对象对应的非线性微分方程,然后,利用Garlerkin逼近方法获得线性化问题的光滑解,从而可以构造出原问题的逼近解.通过估计逼近解的一致有界性,最后证明了一类描述多刚体在不可压缩流体中运动的耦合系统强解的存在性问题.特别要指出的是在初始密度满足相容性条件下,此结论允许流体内部出现真空.

Existence of Strong Solutions for a Class of Fluid-Rigid Coupling System

In this paper,we discuss the existence of strong solutions for a class of fluid-structure interaction systems with multiple rigid bodies and incompressible fluid whose viscosity coefficients depend on density.We 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 by using the Garlerkin approximation method,so that an approximate solution to the original problem can be constructed.By estimating the uniform boundedness of the approximated solution,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.