Nonunique solutions of the transport equation for Sobolev vector fields
Event details
| Date | 22.03.2024 |
| Hour | 14:15 |
| Speaker | Prof. Anuj Kumar (Berkeley) |
| Location | |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract: This talk is based on recent work jointly with E. Bruè and M. Colombo. We construct nonunique
solutions of the continuity equation in the class L^\infty in time and L^rin space. We achieve this by introducing two novel ideas: (1) In the construction, we interweave the scaled copies of
the vector field itself. (2) Asynchronous translation of cubes, which makes the construction
heterogeneous in space. These new ideas allow us to prove nonuniqueness in the range of
exponents beyond what is available using the method of convex integration and sharply match
with the range of uniqueness of solutions from Bruè, Colombo, De Lellis ’21.
Practical information
- General public
- Free
Organizer
- Prof. Maria Colombo
Contact
- Prof. Maria Colombo