| Brenier, Yann (Université de Nice-Sophia-Antipolis) |
Seminarroom C206 + C207 |
Mon, 10. Sep 07, 10:00 |
| Optimal transportation for conservative evolution equations (1/3) |
The relevence of optimal transportation techniques for dissipative
evolution equations is now very well known (following the seminal
paper of Jordan, Kinderlehrer and Otto on the heat equation viewed
as a gradient flow on probability measures for the Boltzmann entropy).
In this minicourse, applications to conservative evolution equations
(such as the Euler equations, multidimensional scalar conservation
laws, Hamilton-Jacobi, ideal MHD...) will be discussed. |
- Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
- Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)
|
| Figalli, Alessio (Scuola Normale di Pisa - École Normale Supérieure de Lyon) |
Seminarroom C206 + C207 |
Mon, 10. Sep 07, 15:00 |
| Incompressible models for the incompressible Euler's
equations (1/2) |
Following Arnold's interpretation, Euler's
equations can be seen as the geodesic equation in the space of
measure preserving diffeomorphism. Thus, one can try to find
solutions to Euler's equation minimizing the Energy functional
with fixed endpoints (this is the usual way to find geodesics
on a manifold). It turns out that the study of (a relaxed
version of) this problem presents many links with optimal
transportation. In this minicourse I will explain the problem
in details, I will review the results of Brenier and
Shnirelman, and I will present recent results obtained in
collaboration with L.Ambrosio. |
- Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
- Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)
|
| Brenier, Yann (Université de Nice-Sophia-Antipolis) |
Seminarroom C206 + C207 |
Tue, 11. Sep 07, 10:00 |
| Optimal transportation for conservative evolution equations (2/3) |
The relevence of optimal transportation techniques for dissipative evolution equations is now very well known (following the seminal paper of Jordan, Kinderlehrer and Otto on the heat equation viewed as a gradient flow on probability measures for the Boltzmann entropy). In this minicourse, applications to conservative evolution equations (such as the Euler equations, multidimensional scalar conservation laws, Hamilton-Jacobi, ideal MHD...) will be discussed. |
- Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
- Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)
|
| Brenier, Yann (Université de Nice-Sophia-Antipolis) |
Seminarroom C206 + C207 |
Wed, 12. Sep 07, 10:00 |
| Optimal transportation for conservative evolution equations (3/3) |
The relevence of optimal transportation techniques for dissipative evolution equations is now very well known (following the seminal paper of Jordan, Kinderlehrer and Otto on the heat equation viewed as a gradient flow on probability measures for the Boltzmann entropy). In this minicourse, applications to conservative evolution equations (such as the Euler equations, multidimensional scalar conservation laws, Hamilton-Jacobi, ideal MHD...) will be discussed. |
- Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
- Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)
|
| Figalli, Alessio (Scuola Normale di Pisa - École Normale Supérieure de Lyon) |
Seminarroom C206 + C207 |
Wed, 12. Sep 07, 15:00 |
| Incompressible models for the incompressible Euler's
equations (2/2) |
Following Arnold's interpretation, Euler's
equations can be seen as the geodesic equation in the space of
measure preserving diffeomorphism. Thus, one can try to find
solutions to Euler's equation minimizing the Energy functional
with fixed endpoints (this is the usual way to find geodesics
on a manifold). It turns out that the study of (a relaxed
version of) this problem presents many links with optimal
transportation. In this minicourse I will explain the problem
in details, I will review the results of Brenier and
Shnirelman, and I will present recent results obtained in
collaboration with L.Ambrosio. |
- Thematic program: Optimal transportation structures, gradient flows and entropy methods for Applied PDEs (2007)
- Event: Summer School "Optimal transportation structures, gradient flows and entropy methods for applied PDE's" (2007)
|