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Dyadic bilinear estimates and applications to the well-posedness for the 2D Zakharov–Kuznetsov equation in the endpoint space 𝐻−1/4

  • Zhaohui Huo EMAIL logo and Yueling Jia
From the journal Forum Mathematicum

Abstract

The Cauchy problem of the 2D Zakharov–Kuznetsov equation tu+x(xx+yy)u+uux=0 is considered. It is shown that the 2D Z-K equation is locally well-posed in the endpoint Sobolev space H-1/4, and it is globally well-posed in H-1/4 with small initial data. In this paper, we mainly establish some new dyadic bilinear estimates to obtain the results, where the main novelty is to parametrize the singularity of the resonance function in terms of a univariate polynomial.

MSC 2010: 35E15; 35Q53

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 11471323

Award Identifier / Grant number: 11571254

Award Identifier / Grant number: 11771444

Funding statement: The first author is supported by NSFC (grant numbers 11471323, 11571254 and 11771444).

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Received: 2020-01-06
Revised: 2020-04-05
Published Online: 2020-08-06
Published in Print: 2020-11-01

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