The Study Of Some Problems Of Navier-Stokes-Poisson Equations

In this paper,we mainly study the "Poisson" term and the property of weak solutions of the Navier-Stokes-Poisson equations in two or three space dimensions.At first,we study the properties of vector functions under the PDE operators by changing the variables of vector functions.We obtain the invariance of the form of vector factions under the effect of the Laplace operator.In order to study the "Poisson" term,by using the boundedness of continuous operators and the results of radically symmetric functions,we obtain the boundedness of this term under the effect of the Riesz operator.On the other hand,under some given conditions of external force function and potential energy function,the formula of unknown vector function is obtained by using Helmholtz decomposition method.Secondly,we study the Navier-Stokes equation in a two dimensional space in the last chapter of this thesis.By considering the definition of weak solutions of Navier-Stokes-Poisson equations,we obtain one property of the weak solution of the Navier-Stokes-Poisson equations in two dimensional space.