Well-posedness for the fifth order KdV equation

2010/11/17 by Takamori Kato, Kato, Takamori
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1011.3956

openalex publication_date 2010/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we establish the well-posedness for the Cauchy problem of the fifth order KdV equation with low regularity data. The nonlinear term has more derivatives than can be recovered by the smoothing effect, which implies that the iteration argument is not available when initial data is given in H^s for any s ∈ ℝ. So we give initial data in H^s,a=H^s ∩ H^a when a ≤ s and a ≤ 0. Then we can use the Fourier restriction norm method to obtain the local well-posedness in H^s,a when s ≥ max\-1/4, -2a-2 \, -3/2

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