Coursebooks

Irregular transport and mixing

MATH-612

Lecturer(s) :

Invited lecturers (see below)

Language:

English

Frequency

Only this year

Remarque

Spring 2021

Summary

We will present the theory of PDEs and of transport equations with rough (non Lipschitz) velocity fields, address both the renormalisation theory by DiPerna-Lions-Ambrosio and its quantitative Lagrangian counterpart and show applications to mixing estimates.

Content

We will present the theory of ODEs and of transport equations with rough (non Lipschitz) velocity fields. We will address both the renormalisation theory by DiPerna-Lions-Ambrosio and its quantitative Lagrangian counterpart. We will show applications to mixing estimates and to properties of solutions of PDEs from fluid dynamics.

 

- The Cauchy-Lipschitz theory in the classical setting

- DiPerna-Lions-Ambrosio renormalisation theory.

- Quantitative estimates for the ODE.

- Mixing and mixing estimates

- Applications to fluid dynamics.

Keywords

ODE flows, transport and continuity equations, Sobolev spaces, mixing, Euler equations

Learning Prerequisites

Recommended courses

Basic classes of analysis, tools from PDE, tools from measure thoery. Some ideas from Fourier analysis or from dynamical systems could be useful.

Resources

Bibliography

Lecture notes and research papers will be communicated during the class.

In the programs

Reference week

 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German