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language
eng
Author
KAMEI, RYOSUKE
Description
This paper studies the Cauchy problem for the nonlinear Schr¨odinger equation i∂tu − ∂2 xu = f(u) in one space dimension. The nonlinear interaction f(u) is a linear combination of (V ∗x u)u, (V ∗x ¯u)u, (V ∗x u)¯u and (V ∗x ¯u)¯u, where V (x) is a locally integrable function whose Fourier transform satisfies | ˆ V (ξ)| ≲ ⟨ξ⟩−m for some m ≥ 0. The Cauchy problem is well-posed in Hs for s > −(m/2+1/4); furthermore, if f(u) contains only the first and the last types of nonlinear terms, then the Cauchy problem is well-posed for s > −(m/2+3/4). The proof is based on bilinear estimates in Xs,b spaces.
Journal Title
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
Volume
57
Start Page
27
End Page
38
ISSN
1342-7121
Published Date
2024
DOI(SelfDOI)
Publisher
総合理工学部
Publisher Aalternative
The Interdisciplinary Graduate School of Science and Engineering
NII Type
Departmental Bulletin Paper
Format
PDF
Text Version
出版社版
OAI-PMH Set
Faculty of Science and Engineering
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