  This is the first of two papers, in which we prove some properties of the
Webster scalar curvature flow. More precisely, we establish the long-time
existence, L^p convergence and the blow-up analysis for the solution of the
flow. As a by-product, we prove the convergence of the CR Yamabe flow on the CR
sphere. The results in this paper will be used to prove a result of prescribing
Webster scalar curvature on the CR sphere, which is the main result of the
second paper.
