We prove that the Itô map, that is the map that gives the solution of a differential equation controlled by a rough path of finite $p$-variation with $p\in [2,3)$ is locally Lipschitz continuous in all its arguments and we give some sufficient conditions for global existence for non-bounded vector fields.
"On rough differential equations." Electron. J. Probab. 14 341 - 364, 2009. https://doi.org/10.1214/EJP.v14-613