Classical flows of vector fields with exponential or sub-exponential summability
Abstract
We show that vector fields b whose spatial derivative Dx b satisfies a Orlicz summability condition have a spatially continuous representative and are well-posed. For the case of sub-exponential summability, their flows satisfy a Lusin (N) condition in a quantitative form, too. Furthermore, we prove that if Dx b satisfies a suitable exponential summability condition then the flow associated to b has Sobolev regularity, without assuming boundedness of divx b. We then apply these results to the representation and Sobolev regularity of weak solutions of the Cauchy problem for the transport and continuity equations.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Elsevier BV
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202308304838Use this for linking
Review status
Peer reviewed
ISSN
0022-0396
DOI
https://doi.org/10.1016/j.jde.2023.07.005
Language
English
Published in
Journal of Differential Equations
Citation
- Ambrosio, L., Nicolussi Golo, S., & Serra Cassano, F. (2023). Classical flows of vector fields with exponential or sub-exponential summability. Journal of Differential Equations, 372(5), 458-504. https://doi.org/10.1016/j.jde.2023.07.005
License
Copyright© 2023 The Authors. Published by Elsevier Inc.