Self-similar Blow-Up Profiles for Slightly Supercritical Nonlinear Schrodinger Equations

Bahri Yakine; Martel Yvan; Raphael Pierre

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Self-similar Blow-Up Profiles for Slightly Supercritical Nonlinear Schrodinger Equations

机译：用于略微超临界非线性的自我相似的爆破轮廓

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We construct radially symmetric self-similar blow-up profiles for the mass supercritical nonlinear Schrodinger equation i partial derivative(t)u + Delta u + |u|(p-1)u = 0 on R-d, close to the mass critical case and for any space dimension d >= 1. These profiles bifurcate from the ground-state solitary wave. The argument relies on the classical matched asymptotics method suggested in Sulem and Sulem (The nonlinear Schrodinger equation. Selffocusing and wave collapse. Applied mathematical sciences, 139, Springer, New York, 1999) which needs to be applied in a degenerate case due to the presence of exponentially small terms in the bifurcation equation related to the log-log blow-up law observed in the mass critical case.

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来源
《Annales Henri Poincare》 |2021年第5期|共49页
作者
Bahri Yakine; Martel Yvan; Raphael Pierre;
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Univ Victoria Dept Math &

Stat Victoria BC Canada;

Ecole Polytech CMLS CNRS Inst Polytech Paris F-91128 Palaiseau France;

Univ Cambridge Ctr Math Sci DPMMS Wilberforce Rd Cambridge CB3 0WA England;

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正文语种 eng
中图分类理论物理学;
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Self-similar Blow-Up Profiles for Slightly Supercritical Nonlinear Schrodinger Equations

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