  We present a blow-up rate estimate for a solution to the parabolic
Gross-Pitaevskii and related systems on entire space with Sobolev subcritical
nonlinearity. We extend the results of [Y. Giga, S. Matsui and S. Sasayama,
Indiana Univ. Math. J. {53} (2004), 483--514] to the parabolic systems.
