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Asymptotic behavior for the dissipative nonlinear Schrödinger equations under mass supercritical setting

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  • Gaku Hoshino

    (Tokyo Denki University)

Abstract

In this paper, we consider the Cauchy problem for the nonlinear Schrödinger equations. In particular, we show the existence of asymptotically free solutions for the dissipative nonlinear Schrödinger equations under mass supercritical setting $$p\ge 1+4/n$$ p ≥ 1 + 4 / n in $$n\ge 1$$ n ≥ 1 space dimensions with data which belong to the weighted Sobolev space $$H^s_2\cap {\mathcal {F}} H^\gamma _2$$ H 2 s ∩ F H 2 γ for some $$s, \gamma \in (0,1]\cap (0,n/2).$$ s , γ ∈ ( 0 , 1 ] ∩ ( 0 , n / 2 ) . In previous paper Hoshino (J Differ Equ 266:4997–5011, 2019), the existence of asymptotically free solutions for the dissipative nonlinear Schrödinger equations for some $$1+4/(n+2\gamma )

Suggested Citation

  • Gaku Hoshino, 2025. "Asymptotic behavior for the dissipative nonlinear Schrödinger equations under mass supercritical setting," Partial Differential Equations and Applications, Springer, vol. 6(3), pages 1-14, June.
    • Handle: RePEc:spr:pardea:v:6:y:2025:i:3:d:10.1007_s42985-025-00318-1
    DOI: 10.1007/s42985-025-00318-1
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    References listed on IDEAS

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    1. Nakao Hayashi & Chunhua Li & Pavel I. Naumkin, 2016. "Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-7, February.
    2. Nakao Hayashi & Chunhua Li & Pavel I. Naumkin, 2016. "Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
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