The Existence Of Local Strong Solutions For Two Classes Of Fluid-structure Interactions Models

Fluid-structure interactions(FSI),i.e.,the interplay of some movable or de-formable structure with an internal or surrounding fluid,are among the most widespread and most challenging coupled or multi-physics problems.In terms of discipline,FSI problem involves fluid mechanics,material mechanics,elasticity,dynamics and other disciplinary knowledge;in terms of technology,FSI problem is related to biology,petrochemical,aerospace,ocean,ship,geology,road and bridge,machinery and other fields.Therefore,due to the multi-intersection of FSI problem,it has very important applications in many fields.In this dissertation,we mainly investigate the local existence of strong solutions for two types of FSI system.The thesis consists of four chapters:In Chapter 1,we introduce the background,research status of FSI system,the main results obtained in the thesis and some basic knowledge to be used in the follow-up research.In Chapter 2,we study the local well-posedness problem on the magnetohy-drodynamics(MHD)-elastic structure interaction systems where the fluid is rep-resented by the incompressible viscous MHD equation in Euler coordinates and the structure is modeled by the elastic equation with superconductor material in Lagrangian coordinates.The equations are coupled along the moving interface though transmission boundary conditions for velocity,normal stress and magnetic field.The local existence of at least one strong solution in time to the incom-pressible viscous and MHD-structure interaction system is proved in the sense of one suitable Sobolev space by using the careful energy method and Tychonoff fixed point theory combining with penalization and smoothing techniques and by overcoming the difficulties caused by the magnetic field.In Chapter 3,we study the motion of a plate with a certain thickness immers-ing an incompressible viscous fluid in a bounded domain of R~3,which is described by FSI system that couples the fourth order hyperbolic equations and the three-dimensional incompressible Navier-Stokes equations.The FSI system also requires the continuity of the normal component of stress and particle displacement fields along the moving interface.Under the suitable physical conditions on the plate at the moving interface,we obtain the local existence of at least one strong solution to the corresponding FSI system in the sense of one suitable Sobolev space by using penalization techniques,the regularity theory of higher-order elliptic equa-tions and Stokes equations,the careful energy method and Tychonoff fixed point theory.In Chapter 4,we summarize the main results of the thesis,and proposes some problems for further investigation.