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Local well‐posedness of critical nonlinear Schrödinger equation on Zoll manifolds of odd‐growth
Author(s) -
Zhao Tengfei
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3766
Subject(s) - dimension (graph theory) , mathematics , nonlinear system , order (exchange) , space (punctuation) , nonlinear schrödinger equation , pure mathematics , mathematical analysis , schrödinger equation , computer science , physics , quantum mechanics , finance , economics , operating system
In this paper, we study the nonlinear Schrödinger equation on Zoll manifolds with odd order nonlinearities. We will obtain the local well‐poesdness in the critical spaceHs 0( M ) . This extends the recent results in the literature to the Zoll manifolds of dimension d ≥2 with general odd order nonlinearities and also partially improves the previous results in the subcritical spaces of Yang to the critical cases. Copyright © 2015 John Wiley & Sons, Ltd.