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A global weak solution to the Lorentzian harmonic map flow |
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| Authors: | Han Xiaoli Liu Lei Zhao Liang |
| Institution: | 1.Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China ;2.Max Planck Institute for Mathematics in the Sciences, Leipzig, 04103, Germany ;3.School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems of MOE, Beijing Normal University, Beijing, 100875, China ; |
| 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 |
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