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arXiv · 2503.08656

Smoothing effect for third order operators with variable coefficients

Serena Federico·Davide Tramontana
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Abstract

In this work we study the smoothing effect of some variable coefficient operators of the form $D_t-A$, where $A$ is a Weyl-quantized pseudo-differential operator of order $m=2,3$. The class under consideration includes, among others, KdV-type and ultrahyperbolic Schr\"odinger operators. We prove homogeneous and inhomogeneous smoothing estimates and use them to get well-posedness results for some NLIVPs with derivative nonlinearities. Finally, we investigate the so called non-trapping property of the bicharacteristic curves of the principal symbol of our operators.

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Serena Federico, Davide Tramontana. 2025-03-11. Smoothing effect for third order operators with variable coefficients. https://arxiv.org/abs/2503.08656

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