Navier-Stokes-Poisson方程若干问题的研究

发布时间：2018-08-05 10:26

【摘要】：本文主要研究空间维数为2维或3维情形下的Navier-Stokes-Poisson方程组中的“Poisson”项以及该方程组弱解的一些性质。首先,针对向量函数,作变量替换,研究其函数在偏微分算子作用下的性质,得到了函数在拉普拉斯算子作用下的形式不变性。对于“Poisson”项,利用连续性算子的有界性、径向对称函数在梯度和旋度作用下的结果,并将密度和势能函数在有界区域外进行零延拓,最后得到了在Riesz算子的作用下的有界性。另一方面,当外力函数和势能函数满足一定关系时,利用Helmholtz分解等方法,给出了某一类未知向量函数的计算公式。其次,在论文的后面,从一个二维空间中的Navier-Stokes方程入手,结合弱解的定义,得出了二维空间中Navier-Stokes-Poisson方程的弱解的一个性质。
[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.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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