Global well-posedness for the derivative nonlinear Schrodinger equation

• 成果类型: Article
• 署名作者: Bahouri, Hajer; Perelman, Galina
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01113-0
• 发表日期: 2022
• 页码: 639-688
• 关键词: solitary waves; orbital stability; parallel

摘要

This paper is dedicated to the study of the derivative nonlinear Schrodinger equation on the real line. The local well-posedness of this equation in the Sobolev spaces H-s(R) is well understood since a couple of decades, while the global well-posedness is not completely settled. For the latter issue, the best known results up-to-date concern either Cauchy data in H-1/2(R) with mass strictly less than 4 pi or general initial conditions in the weighted Sobolev space H-2,H-2(R) . In this article, we prove that the derivative nonlinear Schrodinger equation is globally well-posed for general Cauchy data in H-1/2(R) and that furthermore the H-1/2 norm of the solutions remains globally bounded in time. The proof is achieved by combining the profile decomposition techniques with the integrability structure of the equation.