ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION  

作　　者：沈彩霞 郭柏灵 

机构地区：[1]Faculty of Science,University of Jiang Su [2]Institute of Applied Physics and Computational Mathematics

出　　处：《Acta Mathematica Scientia》2008年第1期117-127,共11页数学物理学报（B辑英文版）

基　　金：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.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：The Davey-Stewartson equation the Cauchy problem ILL-POSEDNESS 

分 类 号：O175[理学—数学]