Partial Differential Equations applied to fluid mechanics and related problems

本项目旨在研究流体力学偏微分方程及相关数学模型解的规律性和可能的爆破。理解这些模型的性质对数学和科学都是一个基本的挑战。溶液的规律性和稳定性与湍流和相变等复杂的多尺度物理现象密切相关。该项目的主要目标是开发新技术来解决包括反应扩散系统或三维Navier-Stokes系统在内的超临界系统的全局规律性问题。这个研究项目将在对流体力学和化学中涉及的数学的基本理解方面取得一些重大进展。这也将有助于在这一重要领域培养新的研究生。物理模型中数学结构的发现将导致对物理现象本身的更深层次的理解。它还将提供一些关于用于描述物理现象的理论物理模型的有效性限制的信息。

This project is aimed at investigating regularity and possible blow-up of solutions to partial differential equations of fluid mechanics and related mathematical models. Understanding of properties of these models is a fundamental challenge both for mathematics and science. The regularity and stability of the solutions are strongly related to complex multiscale physical phenomena such as turbulence and phase transitions. A principal goal of this project is developing new techniques to tackle the problem of global regularity for super-critical systems including reaction-diffusion systems or the 3D Navier-Stokes system.This research program will make some significant progress in the fundamental understanding of the mathematics involved in fluid mechanics and chemistry. It will help also to train new graduate students in this important field. The discovery of mathematical structure in physical models will lead to a deeper understanding of the physical phenomena themselves. It will also provide some information about the limits of validity of the theoretical physical models that are used to describe physical phenomena.