Year: 2015
Type: preprint
Abstract: We present a divergence free vector field in the Sobolev space $H^1$ such that the flow associated to the field does not belong to any Sobolev space. The vector field is deterministic but constructed as the realization of a random field combining simple elements. This construction illustrates the optimality of recent quantitative regularity estimates as it gives a straightforward example of a well-posed flow which has nevertheless only very weak regularity.
Source: arXiv (Cornell University)
Author: Jabin, Pierre-Emmanuel
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1447958654