两类二维非牛顿流体方程组解的渐近行为

发布时间：2019-04-08 20:04

【摘要】：流体力学在物理学、生物学、大气与海洋科学及航空工业等领域有广泛的应用.非牛顿流体力学是近代流体力学的一个重要分支.本硕士论文研究两类二维不可压非牛顿流体力学方程组解的渐近行为.首先,论文给出了这两类方程组的确定模与确定结点的个数估计.有限的确定模个数表明这两类方程组的解的渐近行为可被它们的解的前有限个傅立叶模的渐近行为所确定,有限的确定结点个数则表明这两类方程组的解的渐近行为可被它们的解在有限个点的渐近行为所确定.然后,论文证明了Ladyzhenskaya流体模型的拉回吸引子与不变测度的存在性.研究结果将为进一步理解非牛顿流体力学方程组解的渐近行为提供参考;同时,由于确定模与确定结点的有限性,为人们进行数值模拟计算提供理论依据.
[Abstract]:Fluid mechanics is widely used in physics, biology, atmosphere and marine science, aviation industry and so on. Non-Newtonian fluid dynamics is an important branch of modern fluid dynamics. In this dissertation, the asymptotic behavior of two kinds of two-dimensional incompressible non-Newtonian hydrodynamics equations is studied. First of all, we give the estimation of the number of definite modules and nodes of these two kinds of equations. The finite number of definite modules indicates that the asymptotic behavior of the solutions of the two systems can be determined by the asymptotic behavior of the first finite Fourier modules of their solutions. The finite number of nodes indicates that the asymptotic behavior of the solutions of the two systems can be determined by the asymptotic behavior of their solutions at finite points. Then, the existence of pull-back attractor and invariant measure of Ladyzhenskaya fluid model is proved. The results will provide a reference for further understanding the asymptotic behavior of the solution of the system of non-Newtonian fluid dynamics, and provide a theoretical basis for the numerical simulation calculation due to the finiteness of the determining module and the definite node.
【学位授予单位】：温州大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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