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arXiv · 2510.18168

Remarks on the derivation of the virial identity for nonlinear Schr\"odinger equations

Tomoyuki Ikeda·Shuji Machihara·Hayato Miyazaki·Tohru Ozawa
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Abstract

We revisit the derivation of the virial identity for nonlinear Schr\"odinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were derived without constructing a sequence of approximate solutions. Their approach involves additional properties of solutions due to Strichartz' estimate. In this paper, we derive the virial identity without constructing the sequence of approximate solutions or employing a regularizing argument for weights, by exploiting the properties of solutions.

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Tomoyuki Ikeda, Shuji Machihara, Hayato Miyazaki, Tohru Ozawa. 2025-10-20. Remarks on the derivation of the virial identity for nonlinear Schr\"odinger equations. https://arxiv.org/abs/2510.18168

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