# Spring 2021 MATH 279 002 LEC

Section | Days/Times | Location | Instructor | Class |
---|---|---|---|---|

002 LEC | MoWeFr 10:00AM - 10:59AM | Internet/Online | Thomas Alazard | 33026 |

Units | Enrollment Status | Session |
---|---|---|

4 | Open | 2021 Spring, January 19 - May 07 |

**Prerequisites**

**Description** A classical subject in the mathematical theory of hydrodynamics consists in studying the evolution of the free surface separating the air from a perfect incompressible fluid. We will examine this problem for two important sets of equations: the water wave equations and the Hele-Shaw equations, including the Muskat problem. They are of different nature, dispersive versus parabolic, but we will see that they can be studied by related tools.

These courses are intended for graduate students with a general interest in analysis and no pre-requisites about any advanced theory is required. A large part of the courses will consist of short self-contained introductions to the following topics: Paradifferential calculus, the fractional Laplacian and the multiplier methods of Morawetz and Lions. These lectures also aim to give a self-contained introduction to certain aspects at the cutting edge of research. I will give a detailed analysis of the Cauchy problem for the water wave, Hele-Shaw and Muskat equations.

**Office**

**Office Hours**

**Required Text** None. Professor Alazard will type lecture notes and post them every week on his webpage.

**Recommended Reading**

**Grading** Letter grade.

**Homework**

**Course Webpage**