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J.-M. Coron proved in [5] that the global weak solutions of the heat flowfrom $M$ to $N$, starting at non-stationary weakly harmonic maps, are notunique when $M = B^3$ and $N = S^2$. Hence, the semigroup property of thesolution map does not hold in general. The present short paper uses thetechniques developed by J. Cardona and L. Kapitanski to show the existence ofinfinitely many measurable semigroups solving the heat flow in the same caseswhere non-uniqueness was shown by J.-M. Coron.

Measurable Semigroup Selection of the Heat Flow for Harmonic Maps