Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1768-1781.

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The Ill-Posedness of the Solution for the General Power Derivative Schrödinger Equation in Hs

Chen Xingfa, Zhong Penghong   

  1. School of Mathematics, Guangdong University of Education, Guangzhou 510303
  • Received:2021-06-23 Revised:2022-08-06 Published:2022-12-16
  • Supported by:
    Supported by National Science Foundation for Young Scientists of China(11601092), the Special Projects in Key Fields of Ordinary Colleges and Universities in Guangdong Province(ZDZX1088) and the Fund for Science and Technology of Guangzhou(202102080428)

Abstract: The nonlinear defocusing Schrödinger equations with general power nonlinearity are proved to be ill-posed in the Sobolev space Hs whenever the exponent $s$ is lower than $1/k$ ($2 \leq k \leq 4$) or $1/2-1/k$ ($k>4$).

Key words: Ill-posedness, DNLS-type equations, Regularity

CLC Number: 

  • O175.29