| File | |
| Title |
WELL-POSEDNESS OF QUADRATIC HARTREE TYPE EQUATIONS BELOW L2
|
| Creator |
KAMEI RYOSUKE
|
| Source Title |
島根大学総合理工学部紀要.シリーズB
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics
|
| Volume | 57 |
| Start Page | 27 |
| End Page | 38 |
| Journal Identifire |
ISSN 1342-7121
|
| Descriptions |
Abstract
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.
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| Language |
eng
|
| Resource Type | departmental bulletin paper |
| Publisher |
総合理工学部
The Interdisciplinary Graduate School of Science and Engineering
|
| Date of Issued | 2024 |
| Publish Type | Version of Record |
| Access Rights | open access |
| Relation |
ソウゴウ リコウ ガクブ
|
