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arXiv · 1403.2537

Kato smoothing and Strichartz estimates for wave equations with magnetic potentials

Piero D'Ancona
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Abstract

Let $H$ be a selfadjoint operator and $A$ a closed operator on a Hilbert space $\mathcal{H}$. If $A$ is $H$-(super)smooth in the sense of Kato-Yajima, we prove that $AH^{-\frac14}$ is $\sqrt{H}$-(super)smooth. This allows to include wave and Klein-Gordon equations in the abstract theory at the same level of generality as Schr\"{o}dinger equations. We give a few applications and in particular, based on the resolvent estimates of Erdogan, Goldberg and Schlag \cite{ErdoganGoldbergSchlag09-a}, we prove Strichartz estimates for wave equations perturbed with large magnetic potentials on $\mathbb{R}^{n}$, $n\ge3$.

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Piero D'Ancona. 2014-03-11. Kato smoothing and Strichartz estimates for wave equations with magnetic potentials. https://doi.org/10.1007/s00220-014-2169-8

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