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Wave maps on
$(1{+}2)$-dimensional curved spacetimes
Cristian Gavrus, Casey Jao and Daniel Tataru |
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Vol. 14 (2021), No. 4, 985–1084
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Abstract |
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We initiate the study of -dimensional wave maps on a curved space time in the low-regularity setting. Our main result asserts that in this context the wave maps equation is locally well-posed at almost critical regularity. As a key part of the proof of this result, we generalize the classical optimal bilinear estimates for the wave equation to variable coefficients by means of wave packet decompositions and characteristic energy estimates. This allows us to iterate in a curved space. |
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Keywords
wave maps, curved spacetimes, low regularity, wave packets
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Mathematical Subject Classification 2010
Primary: 35L05, 35L15, 35L70
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Milestones
Received: 7 January 2019
Revised: 22 August 2019
Accepted: 9 December 2019
Published: 6 July 2021
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Authors |
| Cristian Gavrus | |
| Department of Mathematics Johns Hopkins University Baltimore, MD United States |
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| Casey Jao | |
| Department of Mathematics University of California Berkeley, CA United States |
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| Daniel Tataru | |
| Department of Mathematics University of California Berkeley, CA United States |
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