| Title:
|
Unconditional uniqueness of higher order nonlinear Schrödinger equations (English) |
| Author:
|
Klaus, Friedrich |
| Author:
|
Kunstmann, Peer |
| Author:
|
Pattakos, Nikolaos |
| Language:
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English |
| Journal:
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Czechoslovak Mathematical Journal |
| ISSN:
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0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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71 |
| Issue:
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3 |
| Year:
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2021 |
| Pages:
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709-742 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show the existence of weak solutions in the extended sense of the Cauchy problem for the cubic fourth order nonlinear Schrödinger equation with the initial data $u_{0}\in X$, where $X\in \{M_{2,q}^{s}(\mathbb {R}), H^{\sigma }(\mathbb {T}), H^{s_{1}}(\mathbb {R})+H^{s_{2}}(\mathbb {T})\}$ and $q\in [1,2]$, $s\geq 0$, or $\sigma \geq 0$, or $s_{2}\geq s_{1}\geq 0$. Moreover, if $M_{2,q}^{s}(\mathbb {R})\hookrightarrow L^{3}(\mathbb {R})$, or if $\sigma \geq \frac 16$, or if $s_{1}\geq \frac 16$ and $s_{2}>\frac 12$ we show that the Cauchy problem is unconditionally wellposed in $X$. Similar results hold true for all higher order nonlinear Schrödinger equations and mixed order NLS due to a factorization property of the corresponding phase factors. For the proof we employ the normal form reduction via the differentiation by parts technique and build upon our previous work. (English) |
| Keyword:
|
normal form method |
| Keyword:
|
modulation space |
| Keyword:
|
unconditional uniqueness |
| Keyword:
|
higher order nonlinear Schrödinger |
| MSC:
|
35A01 |
| MSC:
|
35A02 |
| MSC:
|
35D30 |
| MSC:
|
35J30 |
| idZBL:
|
07396193 |
| idMR:
|
MR4295241 |
| DOI:
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10.21136/CMJ.2021.0078-20 |
| . |
| Date available:
|
2021-08-02T08:04:35Z |
| Last updated:
|
2023-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149052 |
| . |
| Reference:
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