Model And Analysis Of A Rigid Body Floating In A Viscous Fluid

In this thesis,a model of the vertical motion of rigid body floating in viscous fluids in three-dimensional space is established,then the well-posedness problem of the solution of this model is studied,and an optimal control problem of this model acted on the rigid body is studied.In Chapter 2,the Hamiltonian minimum action principle is used to derive the system of solid-fluid coupling,and in this model,the entropy variation of the fluid is used to introduce viscosity into the system.Chapters 3 and 4 start from the conservation law to verify whether the obtained coupling system conforms to the motion law of fluids.Chapters 5 to 7 mainly consider the well-posedness of the coupled system,including the properties of local existence and uniqueness of solutions,and the properties of global existence and uniqueness of solutions to the system in the sense of small initial values.Chapter 8 of this thesis introduces a class of optimal control problems whose control is acting on the solid,the existence and uniqueness of the optimal control is obtained.Open problems will be proposed in the end of the thesis.