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A global weak solution to the Lorentzian harmonic map flow

  • Xiaoli Han
  • Lei Liu
  • Liang ZhaoEmail author
Articles

Abstract

We investigate a parabolic-elliptic system which is related to a harmonic map from a compact Riemann surface with a smooth boundary into a Lorentzian manifold with a warped product metric. We prove that there exists a unique global weak solution for this system which is regular except for at most finitely many singular points.

Keywords

harmonic map heat flow Lorentzian manifold warped product blow up weak solution 

MSC(2010)

53C43 58E20 

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Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11471014 and 11471299) and the Fundamental Research Funds for the Central Universities. The authors are grateful to the anonymous referees for their careful reading of the manuscript and many helpful suggestions.

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  3. 3.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems of MOEBeijing Normal UniversityBeijingChina

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