Nonlinear wave equations with slowly decaying initial data

Abstract

New local smoothing estimates in Besov spaces adapted to the half-wave group are proved via ${\ell }^2$-decoupling. We apply these estimates to obtain new well-posedness results for the cubic nonlinear wave equation in two dimensions. The results are compared to new well-posedness results in $L^p$-based Sobolev spaces.

arXiv comment30 pages, revised version, accepted to JDE

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Cited by in corpus (2)

• Local smoothing and Hardy spaces for Fourier integral operators
• Local smoothing and Hardy spaces for Fourier integral operators on manifolds