Norm inflation and ill-posedness for the Fornberg-Whitham equation

2022/09/16 by Jinlu Li, Li, Jinlu, Desheng Wu +5
Mathematics · Physics and Astronomy · #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.2209.07865

openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the Cauchy problem for the Fornberg-Whitham equation is not locally well-posed in B^s_p,r(\R) with (s,p,r)∈ (1,1+\frac1p)×[2,∞)× [1,∞] or (s,p,r)∈ \1\×[2,∞)× [1,2] by showing norm inflation phenomena of the solution for some special initial data.

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