Pointwise descriptions of nearly incompressible vector fields with bounded curl
Abstract
Among those nearly incompressible vector fields ${\bf{v}}:{\mathbb{R}}^n\to{\mathbb{R}}^n$ with $|x|\log|x|$ growth at infinity, we give a pointwise characterization of the ones for which $\operatorname{curl}{\bf{v}}= D{\bf{v}}-D^t{\bf{v}}$ belongs to $L^\infty$. When $n=2$ we can go further and describe, still in pointwise terms, the vector fields ${\bf{v}}:{\mathbb{R}}^2\to{\mathbb{R}}^2$ for which $|\operatorname{div}{\bf{v}}|+|\operatorname{curl}{\bf{v}}|\in L^\infty$.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2020
- DOI:
- 10.48550/arXiv.2007.00918
- arXiv:
- arXiv:2007.00918
- Bibcode:
- 2020arXiv200700918C
- Keywords:
-
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Analysis of PDEs;
- 30C65;
- 30C99;
- 34A26;
- 35Q31;
- 42B37