Wave maps on (1+2)-dimensional curved spacetimes
arXiv:1810.05632 · doi:10.2140/apde.2021.14.985
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.
100 pages, 1 figure