Local well-posedness for the Zakharov-Kuznetsov equation in Sobolev spaces

Satoshi Osawa

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arXiv · 2207.04657

Local well-posedness for the Zakharov-Kuznetsov equation in Sobolev spaces

Satoshi Osawa

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Abstract

The initial value problem for two-dimensional Zakharov-Kuznetsov equation on periodic boundary setting is shown to be locally well-posed in the cylinder for 9/10 < s < 1. We prove this theorem by using bilinear estimates thinking separetely the first variable and the second variable of space.

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Satoshi Osawa. 2022-07-11. Local well-posedness for the Zakharov-Kuznetsov equation in Sobolev spaces. https://arxiv.org/abs/2207.04657

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