Summer Graduate School

Fluid-flow stream function color-coded by vorticity in 3D flat torus calculated by K. Nakai (The University of Tokyo)

This school is offered in partnership with the National Center for Theoretical Sciences.

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

General prerequisites:

• H. Brezis, 
  Functional analysis, Sobolev spaces and partial differential equations. 
  Springer, New York, 2011. 
  ISBN: 978-0-387-70913-0
• L. C. Evans, 
  Partial differential equations. Second edition. 
  Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010. 
  ISBN: 978-0-8218-4974-3
• J. C. Robinson, J. L. Rodrigo, & W. Sadowski,
  The three-dimensional Navier--Stokes equations: classical theory.
  Cambridge University Press, 2016.
  ISBN: 978-1107019669

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

Due to the small number of students supported by MSRI, only one student per institution will be funded by MSRI.