Well-posedness of the transport of normal currents by time-dependent vector fields

Paolo Bonicatto; Giacomo Del Nin

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arXiv · 2504.15974

Well-posedness of the transport of normal currents by time-dependent vector fields

Paolo Bonicatto·Giacomo Del Nin

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Abstract

We prove existence and uniqueness for the transport equation for currents (Geometric Transport Equation) when the driving vector field is time-dependent, Lipschitz in space and merely integrable in time. This extends previous work where well-posedness was shown in the case of a time-independent, Lipschitz vector field. The proof relies on the decomposability bundle and requires to extend some of its properties to the class of functions that in one direction are only absolutely continuous, rather than Lipschitz.

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Paolo Bonicatto, Giacomo Del Nin. 2025-04-22. Well-posedness of the transport of normal currents by time-dependent vector fields. https://arxiv.org/abs/2504.15974

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