Vol. 14, No. 4, 2021

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Wave maps on $(1{+}2)$-dimensional curved spacetimes

Cristian Gavrus, Casey Jao and Daniel Tataru

Vol. 14 (2021), No. 4, 985–1084
Abstract

We initiate the study of (1+2)-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 L2 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 Xs,b space.

Keywords
wave maps, curved spacetimes, low regularity, wave packets
Mathematical Subject Classification 2010
Primary: 35L05, 35L15, 35L70
Milestones
Received: 7 January 2019
Revised: 22 August 2019
Accepted: 9 December 2019
Published: 6 July 2021
Authors
Cristian Gavrus
Department of Mathematics
Johns Hopkins University
Baltimore, MD
United States
Casey Jao
Department of Mathematics
University of California
Berkeley, CA
United States
Daniel Tataru
Department of Mathematics
University of California
Berkeley, CA
United States