带有分层效应的二维Euler-Boussinesq模型的整体适定性

发布时间：2018-12-14 02:49

【摘要】：本文主要研究了如下带有分层效应的二维不可压缩Euler-Boussinesq方程的Cauchy问题:其中u = u(t,x)=(u1(t,x),u2(t,x)),θ =(t,x)分别代表流体的速度和温度,标量函数p = p(t,x)代表压力.κ(·)表示热传导系数,在这里,我们假设κ是一个光滑函数,并且满足其中CO0是某一固定的正常数.θe2表示浮力,-u2N2(x2)表示分层效应.其中,实的频率N(x2)(?)√T'0(x2)被称作浮力或者Brunt-Vaisara频率(分层变量),T0(x2)表示线性均值温度剖面函数.本文主要研究带有分层效应的Euler-Boussinesq方程的Cauchy问题(0.1),得到了在没有任何小初值假设条件下,该模型的整体适定性.各章内容安排如下:第一章:简单的叙述了研究Boussinessq方程的背景以及国内外关于这方面的研究进展;第二章:首先列出了文中所需要的相关的定义以及符号,然后给出了本文在证明时所需要的定理和引理;第三章:证明了带有分层效应的Euler-Boussinessq方程Cauchy问题(0.1)的整体适定性.
[Abstract]:In this paper, we mainly study the Cauchy problem of two-dimensional incompressible Euler-Boussinesq equation with delamination effect: where u = u (TX) = (U1 (TX), U2 (TX), 胃 = (t), X) represents the velocity and temperature of the fluid, and the scalar function p = p (t0 x) represents the pressure. 魏 () denotes the heat conduction coefficient. Here, we assume that 魏 is a smooth function. 胃 e 2 denotes buoyancy, and-u2N2 (x 2) denotes delamination effect. Where the real frequency N (x 2) (?) is called buoyancy or Brunt-Vaisara frequency (stratified variable), and T 0 (x 2) denotes a linear mean temperature profile function. In this paper, we study the Cauchy problem (0. 1) of Euler-Boussinesq equation with delamination effect, and obtain the global fitness of the model without any small initial value hypothesis. The contents of each chapter are arranged as follows: chapter 1: the background of the study of Boussinessq equation and the research progress in this field at home and abroad are briefly described. Chapter two: firstly, the necessary definitions and symbols are listed, and then the necessary theorems and Lemma are given. In chapter 3, we prove the global fitness of Cauchy problem (0.1) for Euler-Boussinessq equation with delamination effect.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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