## The weak solutions to the evolution problems of harmonic maps.(English)Zbl 0685.58015

The author proves the existence of global weak solution to the evolution problem of harmonic maps of a compact Riemannian manifold M into the Euclidean n-sphere $$S^ n$$, i.e. the existence of a distribution solution of $$\partial_ tu-\Delta_ Mu+| u_*|^ 2u=0$$, $$t>0$$, $$| u|^ 2=1$$, with $$u(0,.)=u_ 0\in H^{1,2}(M)$$ that is $$L^{\infty}$$-bounded and weakly continuous in $$t>0$$ with values in $$H^{1,2}(M)$$.
Reviewer: G.Tóth

### MSC:

 5.8e+21 Harmonic maps, etc.
Full Text:

### References:

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