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arXiv · 2401.00453

Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces

Satoshi Osawa·Hideo Takaoka
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Abstract

We prove that the Zakharov-Kuznetsov equation on cylindrical spaces is globally well-posed below the energy norm. As is known, local well-posedness below energy space was obtained by the first author. We adapt I-method to extend the solutions globally in time. Using modified energies, we obtain the polynomial bounds on the $H^s$ growth for the global solutions.

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Satoshi Osawa, Hideo Takaoka. 2023-12-31. Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces. https://arxiv.org/abs/2401.00453

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