Dynamics of Partial Differential Equations

Volume 16 (2019)

Number 4

Localization estimate and global attractor for the damped and forced Zakharov–Kuznetsov equation in $\mathbb{R}^2$

Pages: 317 – 323

DOI: https://dx.doi.org/10.4310/DPDE.2019.v16.n4.a1

Authors

Nobu Kishimoto (R.I.M.S., Kyoto University, Kyoto, Japan)

Minjie Shan (School of Mathematical Sciences, Peking University, Beijing, China; and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Yoshio Tsutsumi (Department of Mathematics, Kyoto University, Kyoto, Japan)

Abstract

In the present paper, we show that solutions are spatially localized for the damped and forced Zakharov–Kuznetsov equation in $\mathbb{R}^2$. This result leads to the global attractor in the strong topology of the Sobolev space without weight.

Keywords

Zakharov–Kuznetsov equation, global attractor, Sobolev space

2010 Mathematics Subject Classification

Primary 35B41, 35Q53. Secondary 35B45, 35Q35.

Full Text (PDF format)

The first author N.K. is partially supported by JSPS KAKENHI Grant-in-Aid for Young Researchers (B) (16K17626).

The third author Y.T. is partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B) (17H02853) and Grant-in-Aid for Exploratory Research (16K13770).

Published 30 August 2019