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.

本项目涉及量子力学、几何光学和流体力学中产生的偏微分方程的分析。更具体地说，它侧重于一方面，非线性Schrödinger和非线性波动方程（作为色散方程的模型），另一方面，Navier-Stokes, Boussinesq，原始方程和相关的流体模型。尽管流体模型的建模、物理和计算部分发展得非常好，但数学研究似乎没有遵循同样的进展。与此同时，在过去的二十年中，色散偏微分方程的分析取得了巨大的进展。这就引出了一个很自然的问题如何利用这些新技术和工具来进一步分析来自流体动力学的偏微分方程。在最近的几次尝试中，我们已经可以看到这种趋势的开端。因此，这个项目的总体目的是将这些看似不同的偏微分方程分析的思想和技术结合起来，以便在对湍流和许多其他相关物理现象的数学理解上取得进展。