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.
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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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Han, X., Liu, L. & Zhao, L. A global weak solution to the Lorentzian harmonic map flow. Sci. China Math. 63, 155–166 (2020). https://doi.org/10.1007/s11425-018-9304-1
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DOI: https://doi.org/10.1007/s11425-018-9304-1