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Summer Graduate School

MSRI-NCTS Joint Summer School: Recent Topic in Well Posedness July 18, 2022 - July 29, 2022
Parent Program: --
Organizers Jungkai Chen (National Taiwan University), Mimi Dai (University of Illinois at Chicago), Yoshikazu Giga (University of Tokyo), Tsuyoshi Yoneda (Hitotsubashi University)
Lecturer(s)

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Speaker(s)

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Description
Image
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

 

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.

Keywords and Mathematics Subject Classification (MSC)
Tags/Keywords
  • Euler equations

  • Navier-Stokes equations

  • scaling invariant

  • critical space

  • norm inflation phenomena

  • Fourier splitting method

  • weak solution.

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification
Schedule, Notes/Handouts & Videos
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Jul 18, 2022
Monday
08:45 AM - 09:00 AM
  Introduction
09:00 AM - 10:15 AM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session
Jul 19, 2022
Tuesday
09:00 AM - 10:15 AM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session
Jul 20, 2022
Wednesday
09:00 AM - 10:15 AM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 04:30 PM
  Break
Jul 21, 2022
Thursday
09:00 AM - 10:15 AM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session
Jul 22, 2022
Friday
09:00 AM - 10:15 AM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session
Jul 25, 2022
Monday
09:00 AM - 10:15 AM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session
Jul 26, 2022
Tuesday
09:00 AM - 10:15 AM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 1
Lorenzo Brandolese (Universite Lyon 1)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 04:30 PM
  Student Presentations
Jul 27, 2022
Wednesday
09:00 AM - 12:00 PM
  Student Presentations
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 04:30 PM
  Break
Jul 28, 2022
Thursday
09:00 AM - 10:15 AM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 2
Sylvie Monniaux (Aix-Marseille Université)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 04:30 PM
  Student Presentations
Jul 29, 2022
Friday
09:00 AM - 10:15 AM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
10:15 AM - 10:45 AM
  Break
10:45 AM - 12:00 PM
  Lecture 3
Tsuyoshi Yoneda (Hitotsubashi University)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:00 PM
  Question and Answer
02:00 PM - 03:00 PM
  Problem and Discussion Session
03:00 PM - 03:30 PM
  Break
03:30 PM - 04:30 PM
  Problem and Discussion Session