Abstract
In this article we investigate the issue of local well-posedness for quasilinear wave equations in ℝ2+1 with rough initial data. Our work extends the geometric methods pioneered by Klainerman and Klainerman-Rodniandski for similar problems in ℝ3+1. The main new ingredient of the argument is the use of two new vectorfields, the scaling vectorfield S and the angular momentum vectorfield Ω, which complement the decay information provided by the Morawetz vectorfield K.
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