On the correct definition of the flow of a discontinuous solenoidal vector field

• Date: 2019
• Main Authors: Noarov, A. I., Ноаров, А. И.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1505
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.51 We prove inequalities connecting a flow through the $(n- 1)$-dimensional surface $S$ of a smooth solenoidal vector field with its $L^{p}(U)$-norm ($U$ is an $n$-dimensional domain that contains $S$). On the basis of these inequalities, we propose a correct definition of the flow through...