Abstract
We use a wave packet transform and weighted norm estimates in phase space to establish propagation of singularities for solutions to time-dependent scalar hyperbolic equations that have coefficients of limited regularity. It is assumed that the second order derivatives of the principal coefficients belong to Lt1Lx∞, and that u is a solution to the homogeneous equation of global Sobolev regularity s0=0 or 1. It is then proven that the Hs0+1 wavefront set of u is a union of maximally extended null bicharacteristic curves.
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