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arXiv · 2509.23551

Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows

Robert Schippa·Daniel Tataru
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Abstract

The goal of this paper is to prove bilinear $L^p$ estimates for rough dispersive evolutions satisfying non-degeneracy and transversality assumptions. The estimates generalize the sharp Fourier extension estimates for the cone and the paraboloid. To this end, we require a wave packet decomposition with localization properties in space-time and space-time frequencies. Secondly, we construct a refined wave packet parametrix for dispersive equations with $C^{1,1}$-coefficients by using the FBI transform. As a consequence, we obtain bilinear estimates for solutions to dispersive equations with $C^{1,1}$ coefficients provided that the solutions interact transversely.

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Robert Schippa, Daniel Tataru. 2025-09-28. Wave packet decompositions and sharp bilinear estimates for rough Hamiltonian flows. https://arxiv.org/abs/2509.23551

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