Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
Analysis of PDEs
2017-01-18 v1 Classical Analysis and ODEs
Abstract
We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function.
Keywords
Cite
@article{arxiv.1701.04603,
title = {Well-posedness for the continuity equation for vector fields with suitable modulus of continuity},
author = {Albert Clop and Heikki Jylhä and Joan Mateu and Joan Orobitg},
journal= {arXiv preprint arXiv:1701.04603},
year = {2017}
}