Low regularity data for the periodic Kawahara equation

2012/03/10 by Takamori Kato, Kato, Takamori
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1203.2275

openalex publication_date 2012/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the well-posedness for the Cauchy problem of the Kawahara equation with low regularity data in the periodic case. We obtain the local well-posedness for s ≥ -3/2 by a variant of the Fourier restriction norm method. On the other hand, we show the ill-posedness for s

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