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ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION
作者姓名:沈彩霞  郭柏灵
作者单位:[1]Faculty of Science, University of Jiang Su, Zhenjiang 212013, China [2]Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
基金项目:This work is supported by the Science Foundation of Jiangsu University (07JDG038)
摘    要:The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.

关 键 词:戴维方程式  柯西问题  非线性  数学
收稿时间:2005-11-23
修稿时间:2006-08-22

Ill-Posedness for the Nonlinear Davey-Stewartson Equation
Shen Caixia,Guo Boling.ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION[J].Acta Mathematica Scientia,2008,28(1):117-127.
Authors:Shen Caixia  Guo Boling
Institution:aFaculty of Science, University of Jiang Su, Zhenjiang 212013, China;bInstitute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract:The nonlinear D-S equations on Rd, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space Hs whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.
Keywords:The Davey-Stewartson equation  the Cauchy problem  ill-posedness
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