Sharp ill-posedness results for the KdV and mKdV equations on the torus

2011/05/18 by Luc Molinet, Molinet, Luc
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.1105.3601

openalex publication_date 2011/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a new a priori bound for L² -bounded sequences of solutions to the mKdV equations on the torus. This first enable us to construct weak solutions in L² for this equation and to check that the "solutions" constructed by Kappeler and Topalov in the defocusing case satisfy the equation in some weak sense. In a second time, we prove that the solution-map associated with the mKdV and the KdV equation are discontinuous for the H^s(\T) topology for respectively s<0 and s

Citations

• Multilinear estimates for periodic KdV equations, and applications

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