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

  • A. I. Noarov

Abstract

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 the surface $S$ of a discontinuous solenoidal vector field $f \in L^{p}(U)$ (or, more precisely, of the class of vector fields that are equal almost everywhere with respect to the Lebesque measure).
Published
25.08.2019
How to Cite
NoarovA. I. “On the Correct Definition of the Flow of a Discontinuous Solenoidal Vector Field”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, no. 8, Aug. 2019, pp. 1141-9, http://umj.imath.kiev.ua/index.php/umj/article/view/1505.
Section
Short communications