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

Gaku Hoshino ()
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Gaku Hoshino: Tokyo Denki University

Partial Differential Equations and Applications, 2025, vol. 6, issue 3, 1-14

Abstract: 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 )

Keywords: Nonlinear Schrödinger equations; Dissipative nonlinearity; Asymptotic behavior; Scattering; 35Q55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00318-1

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