The Blowup Mechanism Of The Solution To Navier-Stokes-Landau-Lifshitz System

Ferromagnetic fluid is a new functional material owing both the fluidity of fluid and the magnetism of solid magnetic material and a stable gelled fluid composed of magnetic solid particles with a diameter of nanometers,base carrier fluid and interfacial active agent.The magnetism of the fluid disappears in static state but shows when the external magnetic field is applied.In Chapter 1,the physical background and the research status of the in-compressible Navier-Stokes-Landau-Lifshitz system and the compressible quantum Navier-Stokes-Landau-Lifshitz system,and the notations and the inequalities are introduced.In Chapter 2,the blow-up criteria to the Cauchy problem of the incompressible Navier-Stokes-Landau-Lifshitz system in two-dimension and three-dimension are researched where the former is established on Lebesgue space,and the latter is established on Lebesgue space,BMO space and the Besov space with negative exponent respectively.In Chapter 3,the investigation shows that the local smooth solutions to the quantum Navier-Stokes-Landau-Lifshitz system in the domainsΩ?R~n(n=1,2)that half-space R_+~n,whole-space R~nand ball will blow up in finite time.It also shows that the lifespan time of the local smooth solutions in half-space or whole-space only depends on boundary conditions,while depends on initial data and boundary conditions in the ball.The final chapter summarizes the research conclusions.It also points out the limitations of the methods used in this paper.For this reason,other methods need to be sought for further research.