Well-posedness Of Solutions Of Two-dimensional Navier-Stokes Equations And Euler Equations On Bounded Connected Regions

In this paper,we investigate theorem 1 for the two-dimensional incompressible viscous Navier Stokes equation with Coriolis force and the initial boundary value problem in the bounded region,and theorem 2 for the two-dimensional Euler equation with Coriolis force in the bounded multi-connected region.The first chapter mainly reviews the research background and research status of the Navier-Stokes equation and the Euler equation obtained by Navier-Stokes equation under the disappearance of viscosity,and briefly introduces the stream function method of the vorticity equation.In the second chapter,we gives some preliminary knowledge mainly on functional inequalities that will be used in the article.We use the vorticity form of the Navier-Stokes equation to study the well-posed problem of the fluid in the region,that is,when the initial value is?₀(^?X^??)?L¹(7)Q _T(8)(40)C^2,?(7)Q _T(8)in the third chapter,the existence of the solution is obtained by several lemmas and Schauder fixed point theorem,the uniqueness of the solution is obtained by the iterative method and finally the attenuation is proved.In the fourth chapter,we consider the two-dimensional Euler equation with Coriolis force problem by using the stream function method.The main difficulty is that it is not easy to obtain the constraint conditions of the stream function on the boundary and it is solved by using Kelvin velocity circulation theorem.Then the problem is transformed into an initial boundary value problem of hyperbolic elliptic composite type.Before proving the main results,the prior estimates of"quasi Lipschitz"modules are given,and several lemmas and prior estimates are obtained through the characteristics of the equation.Then the well posedness of the solution of Euler equation is obtained.