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 spa… Show more
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