Global Existence of Geometric Rough Flows

Abstract

In this paper we consider rough differential equations on a smooth manifold $\left(M\right).$ The main result of this paper gives sufficient conditions on the driving vector-fields so that the rough ODE's have global (in time) solutions. The sufficient conditions involve the existence of a complete Riemannian metric $\left(g\right)$ on $M$ such that the covariant derivatives of the driving fields and their commutators to a certain order (depending on the roughness of the driving path) are bounded. Many of the results of this paper are generalizations to manifolds of the fundamental results in \cite{Bailleul2015a}.

52 pages with one figure

Cited by in corpus (1)

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