  In my previous paper I have contrived a Ginzburg-Landau heat flow with a
time-dependent parameter and by using it, I constructed a harmonic heat flow
into spheres with a monotonical inequality and a reverse Poincar\'{e}
inequality. This paper establishes these two energy inequalities near the
boundary and then by making the best of them, we discuss a partial boundary
regularity. In addition to it, we demonstrate a whole domain's regularity under
"the one-sided condition." This has been proposed by S.Hildebrandt and
K.-O.Widman.
