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Published online: 2018-12-12
On flows generated by vector fields with compact supportOlivier Kneuss and Wladimir Neves (1) Universidade Federal do Rio de Janeiro, Brazil
(2) Universidade Federal do Rio de Janeiro, Brazil
We are concerned with the theory of the existence and uniqueness of flows generated by divergence free vector fields with compact support. Hence, assuming that the velocity vector fields are measurable, bounded, and the flows in the Euclidean space are measure preserving, we show two counterexamples of uniqueness/existence of such flows. First we consider the autonomous case in dimension 3 and then the non-autonomous one in dimension 2.
Keywords: Flows, existence, uniqueness, compact support
Kneuss Olivier, Neves Wladimir: On flows generated by vector fields with compact support. Port. Math. 75 (2018), 121-157. doi: 10.4171/PM/2013