Two remarks on generalized flows for ordinary differential equations. (Q997968)

The authors refer to the article of \textit{R. J. DiPerna} and \textit{P. L. Lions} [Invent. Math. 961, 511--547 (1989; Zbl 0696.34049)]. In this article, the proofs for existence and uniqueness are based upon the equivalence between the existence and uniqueness of the generalized flow solution and it associated transport equation \(\frac{\partial f}{\partial t}-b\cdot\nabla f=0\). Now, the authors give a self-contained proof of the uniqueness of such a flow. Secondly, they extend the uniqueness statement from the cited article by giving a proof without using the group property of the flow in the time variable. Here, the associated linear transport equation is used.