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In this work we deal with the selection problem of flows of an irregularvector field. We first summarize an example from \cite{CCS} of a vector field$b$ and a smooth approximation $b_\epsilon$ for which the sequence $X^\epsilon$of flows of $b_\epsilon$ has subsequences converging to different flows of thelimit vector field $b$. Furthermore, we give some heuristic ideas on theselection of a subclass of flows in our specific case.

On smooth approximations of rough vector fields and the selection of flows