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 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 L^p(U) (or, more precisely, of the class of vector fields that are equal almost everywhere with respect to the Lebesque measure).