2018/10/08 by Bruce K. Driver, Driver, Bruce K. · 1 citation
Computer Science · Mathematics · #34C40 #34F05 (primary) #60H10 #Advanced Mathematical Modeling in Engineering #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Probability (math.PR) #math.CA #math.DG #math.DS #math.PR #msc:34C40 #msc:34F05 #msc:60H10
paper · pdf · doi:10.48550/arxiv.1810.03708
52 pages with one figure
arxiv created 2018/10/08 · openalex publication_date 2018/10/08 · arxiv updated 2018/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider rough differential equations on a smooth manifold ( M) . 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 ( g) 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 \citeBailleul2015a.