Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 1

Flowbox theorems for a class of Sobolev vector fields

Pages: 23 – 35

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n1.a2


Mário Bessa (Universidade da Beira Interior, Covilhã, Portugal)


We give sufficient conditions for the flowbox theorem for Sobolev vector fields to be valid not only for the general case but also for the conservative case.


Sobolev vector fields, divergence-free vector fields, flowbox theorem

2010 Mathematics Subject Classification

Primary 37C10, 37C15, 46Exx. Secondary 34C40, 35Axx, 37A05.

The author was partially supported by the FCT (Fundação para a Ciência e a Tecnologia) through Centro de Matemática e Aplicações (CMAUBI), by the Universidade da Beira Interior project UID/00212/2020, and by the Project “Means and Extremes in Dynamical Systems” (PTDC/MATPUR/4048/2021). The author also like to thank the CMUP for providing the necessary conditions in which this work was developed.

Accepted 9 October 2022

Published 23 December 2022