On sharp global well-posedness and Ill-posedness for a fifth-order\n KdV-BBM type equation

2018/05/15 by Mahendra Panthee, Panthee, Mahendra, Xavier Carvajal +1
Mathematics · Physics and Astronomy · #35A01 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1805.06039

openalex publication_date 2018/05/15 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem associated to the recently derived higher\norder hamiltonian model for unidirectional water waves and prove global\nexistence for given data in the Sobolev space H^s, s\≥ 1. We also prove\nan ill-posedness result by showing that the flow-map is not continuous if the\ngiven data has Sobolev regularity s< 1. The results obtained in this work are\nsharp.\n

Citations

• The Hydrodynamical Relevance of the Camassa–Holm and Degasperis–Procesi Equations

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