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arxiv: 2302.09954 · v1 · pith:MBX4JFOMnew · submitted 2023-02-20 · 🧮 math.AP

1+2 dimensional radially symmetric wave maps revisit

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keywords smootharbitraryauthordimensionalmanifoldmapsradiallysymmetric
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The author gives an alternative and simple proof of the global existence of smooth solutions to the Cauchy problem for wave maps from the 1+2-dimensional Minkowski space to an arbitrary compact smooth Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. the author can also treat non-compact manifold under some additional assumptions which generalize the existing ones.

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    Proves local well-posedness for Schrödinger map flow from T^d to S^2 at σ > d/2 + 1/2 (d≥3) and to general compact Kähler N at σ > d/2 + 5/6 (d≥2), first such low-regularity result in periodic setting.