arXiv subjects

Satoshi Osawa

Publications and source records attributed to Satoshi Osawa.

2 recordsLinked to original sources

arXiv2023

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

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.

math.AP↗

arXiv2022

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

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.

math.AP↗