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arXiv · 2203.06412

Nonlinear wave equations with slowly decaying initial data

Jan Rozendaal·Robert Schippa
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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.

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Jan Rozendaal, Robert Schippa. 2022-03-12. Nonlinear wave equations with slowly decaying initial data. https://doi.org/10.1016/j.jde.2022.12.022

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