In this paper, we use the modified potential well method to study the long time behaviors of solutions to the heat flow of H‐system in a bounded smooth domain of R2$$ {R}amp;#x0005E;2 $$. Global existence and finite time blowup of solutions are proved when the initial energy is in three cases. When the initial energy is low or critical, we not only give a threshold result for the global existence and blowup of solutions but also obtain the decay rate of the L2$$ {L}amp;#x0005E;2 $$ norm for global solutions. When the initial energy is high, sufficient conditions for the global existence and blowup of solutions are also provided. We extend the recent results which were.
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