Analysis of Mathematical models for the ocean, atmospherics sciences and optics.

海洋、大气科学和光学数学模型分析。

• 批准号: RGPIN-2014-03628
• 负责人: Ibrahim, Slim
• 金额: $ 1.31万
• 依托单位: University of Victoria
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635643
• 关键词: Analysis; Mathematical; models; ocean; atmospherics

This project concerns the analysis of Partial Differential Equations arising from quantum mechanics, geometric optics and fluid mechanic. More specifically, it focuses on the one hand on, the Nonlinear Schrödinger and Nonlinear Wave equations (as models for dispersive equations), and on the other hand on, the Navier-Stokes, Boussinesq, the primitive equations and related fluid models.Although the modeling, physical and the computational parts were very well developed for fluid models, the mathematical study did not seem to follow the same stream of progress. Meanwhile and during the last two decades, a tremendous progress has been made in the analysis of dispersive partial differential equations. So that comes the natural question on how one can use and take advantage of those new techniques and tools to further analyze the partial differential equations coming from fluid dynamic. One can already observe the beginning of this in several recent attempts. So the general purpose of this project is to bring together ideas and techniques from these seemingly different kinds of Analysis of PDEs in order to make progress on the mathematical understanding of turbulence and many other relevant physical phenomena.

该项目涉及量子力学，几何光学和流体机械师产生的部分微分方程的分析。更具体地说，它的重点是一只手，非线性schrödinger和非线性波方程（作为分散方程的模型），另一方面，Navier-Stokes，Boussinesq，原始方程式，原始方程式和相关的流体模型。以及计算部件的模型和计算部件以及数学模型的发展非常好。在过去的二十年中，在分散偏微分方程的分析中取得了巨大进步。因此，这是关于如何利用和利用这些新技术和工具进一步分析来自流体动态的部分微分方程的自然问题。在最近的几次尝试中，人们已经可以观察到这一点的开始。因此，该项目的一般目的是从这些看似不同的PDE分析中汇集思想和技术，以便在湍流和许多其他相关物理现象的数学理解方面取得进展。