Description

The Navier-Stokes (a.k.a. Navier - Stokes - Landau - Lifshitz) equations govern the flow of fluids and are a fundamental result of basic local conservation laws of physics. They find applications from the study of turbulent fluid flows to geoscience. Emerging out of fundamental principles, they are a good description of the dynamics of a vast range of dynamical systems. One of the most surprising facts about them is the connection with General Relativity and the dynamical evolution of black holes. In a more modern sense and in the framework of holography (AdS/CFT) they have strong implications for strongly coupled Quantum Mechanical systems.

This project will explore both the derivation and some of their applications.

Prerequisites

• Analysis in Many Variables II (or PHYS 2611 Mathematical methods in Physics)
• Mathematical Physics II

Resources

• Landau, L. D.; Lifshitz, E. M. (1987), Fluid mechanics, Course of Theoretical Physics 6 (2nd revised ed.), Pergamon Press
• For a brief introduction to the concepts see Wiki
• For the related Millennium Prize Problems page see here.