Global well-posedness for the coupled system of Schrödinger and Kawahara equations

2023/05/02 by Wangseok Shin, Shin, Wangseok
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2305.01504

openalex publication_date 2023/05/02 · openalex created_date 2023/05/04 · openalex updated_date 2026/07/28

Abstract

We study the local and global well-posedness for the coupled system of Schrödinger and Kawahara equations on the real line. The Sobolev space L² × H^-2 is the space where the lowest regularity local solutions are obtained. The energy space is H¹ × H². We apply the Colliander-Holmer-Tzirakis method [7] to prove the global well-posedness in L² × L² where the energy is not finite. Our method generalizes the method of Colliander-Holmer-Tzirakis in the sense that the operator that decouples the system is nonlinear.

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