English

Non-renormalized solutions to the continuity equation

Analysis of PDEs 2018-07-03 v2

Abstract

We show that there are continuous, W1,pW^{1,p} (p<d1p<d-1), incompressible vector fields for which uniqueness of solutions to the continuity equation fails.

Cite

@article{arxiv.1806.09145,
  title  = {Non-renormalized solutions to the continuity equation},
  author = {Stefano Modena and László Székelyhidi},
  journal= {arXiv preprint arXiv:1806.09145},
  year   = {2018}
}

Comments

30 pages; v2: added acknowledgements and corrected some misprints

R2 v1 2026-06-23T02:39:49.183Z