Abstract
We consider the normalized CR Yamabe flow$\frac{\partial\theta (t)}{\partial t} = 2(r(t) - \rho (t)) \theta(t)$, where $\theta (t)$ is a family of contact forms on a closed CRmanifold $M$, $\rho (t)$ denotes its Tanaka-Webster curvatures, and$r(t) = \frac{\int_M \rho(t) \theta(t) \wedge d\theta(t)}{\int_M 1\theta(t) \wedge d\theta(t)}$. We will show this flow has the longtime existence when $M$ is of dimension three. In particular for thescalar negative case and the scalar flat case, we can show theasymptotic convergence for our flow.