On the correct definition of the flow of a discontinuous solenoidal vector field - Noarov, A. I. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
UDC 517.51 We prove inequalities connecting a flow through the $(n- 1)$-dimensional surface $S$ of a smooth solenoidal vector fieldwith 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 the surface $S$ of a discontinuous solenoidal vector field $f \in L^{p}(U)$ (or, moreprecisely, of the class of vector fields that are equal almost everywhere with respect to the Lebesque measure).