On ill-posedness for the one-dimensional periodic cubic Schrodinger equation

2008/06/27 by Luc Molinet, Molinet, Luc
Mathematics · #35A05 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · doi:10.48550/arxiv.0806.4538

openalex publication_date 2008/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the ill-posedness in H^s(\T) , s<0, of the periodic cubic Schrödinger equation in the sense that the flow-map is not continuous from H^s(\T) into itself for any fixed t≠ 0 . This result is slightly stronger than the one obtained by Christ-Colliander-Tao where the discontinuity of the solution map is established. Moreover our proof is different and clarifies the ill-posedness phenomena. Our approach relies on a new result on the behavior of the associated flow-map with respect to the weak topology of L²(\T) .

Citations

• On the ill-posedness of some canonical dispersive equations

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