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On the derivative nonlinear Schrödinger equation with weakly dissipative structure

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Abstract

We consider the initial value problem for cubic derivative nonlinear Schrödinger equation in one space dimension. Under a suitable weakly dissipative condition on the nonlinearity, we show that the small data solution has a logarithmic time decay in \(L^2\).

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Yanbian University, 977 Gongyuan Road, Yanji, 133002, Jilin, China

    Chunhua Li

  2. Department of Mathematics, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka, 560-0043, Japan

    Yoshinori Nishii

  3. Micron Memory Japan, G.K., 7-10 Yoshikawakogyodanchi, Higashihiroshima, Hiroshima, 739-0153, Japan

    Yuji Sagawa

  4. Department of Mathematics, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Hideaki Sunagawa

Authors
  1. Chunhua Li
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  2. Yoshinori Nishii
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  3. Yuji Sagawa
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  4. Hideaki Sunagawa
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Correspondence to Hideaki Sunagawa.

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Dedicated to Professor Akitaka Matsumura on the occasion of his seventieth birthday

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This work is partly supported by Osaka City University Advanced Mathematical Institute (MEXT Joint Usage/Research Center on Mathematics and Theoretical Physics JPMXP0619217849). The work of H. S. is supported by Grant-in-Aid for Scientific Research (C) (No. 17K05322), JSPS.

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Li, C., Nishii, Y., Sagawa, Y. et al. On the derivative nonlinear Schrödinger equation with weakly dissipative structure. J. Evol. Equ. 21, 1541–1550 (2021). https://doi.org/10.1007/s00028-020-00634-6

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  • DOI: https://doi.org/10.1007/s00028-020-00634-6

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