MATH-612 / 2 credits
Teacher: Invited lecturers (see below)
Remark: Spring 2022
Only this year
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.
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.
ODE flows, transport and continuity equations, Sobolev spaces, mixing, Euler equations
Basic classes of analysis, tools from PDE, tools from measure thoery. Some ideas from Fourier analysis or from dynamical systems could be useful.
Lecture notes and research papers will be communicated during the class.
In the programs
- Subject examined: Irregular transport and mixing
- Lecture: 28 Hour(s)