  In this paper, we consider the heat flow for p-pseudoharmonic maps from a
closed Sasakian manifold M into a compact Riemannian manifold N. We prove
global existence and asymptotic convergence of the solution for the
p-pseudoharmonic map heat flow, provided that the sectional curvature of the
target manifold N is nonpositive. Moreover, without the curvature assumption on
the target manifold, we obtain global existence and asymptotic convergence of
the p-pseudoharmonic map heat flow as well when its initial p-energy is
sufficiently small.
