On the Global Well-Posedness and Orbital Stability of Standing Waves for the Schrödinger Equation with Fractional Dissipation

Autor:	Jingqun Wang, Jiangen Liu, Lixin Tian
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	dissipative Schrödinger equation iterative scheme global well-posedness orbital stability Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 7, Iss 7, p 531 (2023)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract7070531
Popis:	In this paper, we are concerned with the nonlinear fractional Schrödinger equation. We extend the result of Guo and Huo and prove that the Cauchy problem of the nonlinear fractional Schrödinger equation is global well-posed in H32−γ(R) with 12≤γ<1. In view of the complexity of the nonlinear fractional Schrödinger equation itself, the local smoothing effect and maximal function estimates are not enough for presenting the global well-posedness for the nonlinear fractional Schrödinger equation. In this paper, we use a suitably iterative scheme and complete the global well-posed result for Equation (R). Moreover, we obtain the orbital stability of standing waves for the above equations via establishing the profile decomposition of bounded sequences in Hs(RN) (0
Databáze:	Directory of Open Access Journals
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