On the Cauchy problem for the periodic fifth-order KP-I equation

2017/12/04 by Tristan Robert, Robert, Tristan
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · doi:10.48550/arxiv.1712.01134

openalex publication_date 2017/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to investigate the Cauchy problem for the periodic fifth order KP-I equation ∂_t u - ∂_x⁵ u -∂_x^-1∂_y²u + u∂_x u = 0,~(t,x,y)∈ℝ×\mathbbT² We prove global well-posedness for constant x mean value initial data in the space 𝔼 = \u∈ L²,~∂_x² u ∈ L²,~∂_x^-1∂_y u ∈ L²\ which is the natural energy space associated with this equation.

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