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Mathematical Sciences Research Institute

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Summer Graduate School

Introduction to water waves July 27, 2020 - August 07, 2020
Parent Program:
Location: MSRI: Simons Auditorium, Atrium
Organizers Mihaela Ifrim (University of Wisconsin-Madison), Daniel Tataru (University of California, Berkeley)
Description
Img 6168
Overturning wave, artistic drawing by E. Ifrim

The goal is to present the main current research directions in water waves. We will begin with the physical derivation of the equations, and present some of the analytic tools needed in study. The final goal will be two-fold, namely (i) to understand the local solvability of the Cauchy problem for water waves, as well as (ii) to describe the long time behavior of solutions.

Through the lectures and associated problem sessions, students will learn about a number of new analysis tools which are not routinely taught in a graduate school curriculum. The goal is to help students acquire the knowledge needed in order to start research in water waves and Euler equations.

Suggested prerequisites:

Students should have read thoroughly the the following references:

1. R. Strichartz: A guide to theory to distribution and Fourier transforms

2. L. C. Evans:  Introduction to partial differential equations: Chapters 1, 2, 5, 6, 7.

3. Terence Tao:  Nonlinear dispersive equations: local and global analysis Chapter 2, and 3

Solving the problems listed at the end of each of the chapters in each of the above books is strongly recommended. 

For eligibility and how to apply, see the Summer Graduate Schools homepage

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • water waves

  • incompressible Euler equations

  • fluid flows

  • free boundaries

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
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