【摘要】：本文主要研究空間維數(shù)為2維或3維情形下的Navier-Stokes-Poisson方程組中的“Poisson”項以及該方程組弱解的一些性質(zhì)。首先,針對向量函數(shù),作變量替換,研究其函數(shù)在偏微分算子作用下的性質(zhì),得到了函數(shù)在拉普拉斯算子作用下的形式不變性。對于“Poisson”項,利用連續(xù)性算子的有界性、徑向?qū)ΨQ函數(shù)在梯度和旋度作用下的結(jié)果,并將密度和勢能函數(shù)在有界區(qū)域外進行零延拓,最后得到了在Riesz算子的作用下的有界性。另一方面,當外力函數(shù)和勢能函數(shù)滿足一定關(guān)系時,利用Helmholtz分解等方法,給出了某一類未知向量函數(shù)的計算公式。其次,在論文的后面,從一個二維空間中的Navier-Stokes方程入手,結(jié)合弱解的定義,得出了二維空間中Navier-Stokes-Poisson方程的弱解的一個性質(zhì)。
[Abstract]:In this paper, we study the term "Poisson" and some properties of weak solutions of Navier-Stokes-Poisson equations with space dimension of two or three dimensions. Firstly, we study the properties of vector function under the action of partial differential operator, and obtain the form invariance of function under the action of Laplace operator. For the term "Poisson", by using the boundedness of continuous operators, the results of radial symmetric functions under the action of gradient and curl, and the zero continuation of density and potential energy functions outside the bounded region, the boundedness under the action of Riesz operator is obtained. On the other hand, when the external force function and the potential energy function satisfy a certain relation, the calculation formula of a certain class of unknown vector function is given by using the method of Helmholtz decomposition and so on. Secondly, starting with the Navier-Stokes equation in a two-dimensional space and combining the definition of the weak solution, a property of the weak solution of the Navier-Stokes-Poisson equation in the two-dimensional space is obtained.
【學(xué)位授予單位】：華僑大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O175

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本文編號：2165513