Abstract
The flow of vector field X is the solution to the system of linear partial differential equations ∂_t u(t,z)=X(u(t,z)) with initial condition u(0,z)=z. It is known that for an analytic vector field, its flow is given by a convergent Lie series. Recently, Carillo gave a quick and elementary proof of this fact by introducing a special family of norms. This paper gives an even more concise proof by directly estimating the formal series expansion and using a family of majorant functions studied by Lax.
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