Video URL
On the flow map and the partial differential equations associated to a non-smooth vector field (Onl…On the flow map and the partial differential equations associated to a non-smooth vector field (Online)
APA
(2024). On the flow map and the partial differential equations associated to a non-smooth vector field (Online). SciVideos. https://youtube.com/live/e-Nk2EbWD4U
MLA
On the flow map and the partial differential equations associated to a non-smooth vector field (Online). SciVideos, Oct. 02, 2024, https://youtube.com/live/e-Nk2EbWD4U
BibTex
@misc{ scivideos_ICTS:29946,
doi = {},
url = {https://youtube.com/live/e-Nk2EbWD4U},
author = {},
keywords = {},
language = {en},
title = {On the flow map and the partial differential equations associated to a non-smooth vector field (Online)},
publisher = {},
year = {2024},
month = {oct},
note = {ICTS:29946 see, \url{https://scivideos.org/icts-tifr/29946}}
}
Abstract
The flow associated to a given smooth vector field $u(t,x)$ is well-defined, it is smooth, and it can be used to solve the classical linear PDEs associated to $u$, namely the transport and the continuity equations. The situation is substantially different when $u$ is not smooth (e.g. when $u$ is not Lipschitz continuous in the space variable, but only Sobolev or BV). Goal of the lecture is to provide an overview on classical and recent results about flow maps and PDEs associated to non-smooth vector fields.