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arXiv · 2608.01440

Local smoothing for rough wave equations

Jan Rozendaal·Robert Schippa
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Abstract

We prove local smoothing estimates for wave equations with $C^{r}$ coefficients, relying on bilinear restriction estimates associated with rough wave propagation. In two and three dimensions, for $C^{1,1}$ coefficients we recover the sharp $L^p$-$L^q$ local smoothing bounds previously established for smooth coefficients. These are implied by stronger $L^{p}$-$L^{q}$ decoupling inequalities with endpoint derivative loss. As a corollary, we obtain non-trivial $L^{p}$-$L^{p}$ local smoothing estimates as well.

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Jan Rozendaal, Robert Schippa. 2026-08-02. Local smoothing for rough wave equations. https://arxiv.org/abs/2608.01440

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