WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

作     者：HUOZHAOHUI JIAYUELING HUO ZHAOHUI JIA YUELING Graduate School, China Academy of Engineering Physics, P. O. Box 2101, Beijing 100088, China. Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China.

作者机构：GraduateSchoolChinaAcademyofEngineeringPhysicsP.O.Box2101Beijing100088China AcademyofMathematicsandSystemSciencesChineseAcademyofSciencesBeijing100080China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2005年第26卷第1期

页      面：75-88页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Fourier restriction norm Trilinear estimates Hirota equation Low regularity Global well-posedness 

摘      要：The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s ≥ -1-4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.