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arXiv · 1810.05632

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

Cristian Gavrus·Casey Jao·Daniel Tataru
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Abstract

In this article we initiate the study of 1+ 2 dimensional wave maps on a curved spacetime 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 L^2 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 X^{s,b} space.

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Cristian Gavrus, Casey Jao, Daniel Tataru. 2018-10-12. Wave maps on (1+2)-dimensional curved spacetimes. https://doi.org/10.2140/apde.2021.14.985

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