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arXiv · 1902.00710

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

Gennaro Ciampa·Gianluca Crippa·Stefano Spirito
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Abstract

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

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Gennaro Ciampa, Gianluca Crippa, Stefano Spirito. 2019-02-02. On smooth approximations of rough vector fields and the selection of flows. https://arxiv.org/abs/1902.00710

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