  In this paper, we study the torsion flow which is served as the CR analogue
of the Ricci flow in a closed pseudohermitian manifold. We show that there
exists a unique smooth solution to the CR torsion flow in a small time interval
with the CR pluriharmonic function as an initial data. In spirit, it is the CR
analogue of the Cauchy-Kovalevskaya local existence and uniqueness theorem for
analytic partial differential equations associated with Cauchy initial value
problems
