A note on global existence for the Zakharov system on $\mathbb{T}
We show that the one-dimensional periodic Zakharov system is globally well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is obtained by combining the I-method with Bourgain's high-low decomposition method. As a corollary, we obtain probabilistic global existence results...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Compaan, E |
| description | We show that the one-dimensional periodic Zakharov system is globally
well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is
obtained by combining the I-method with Bourgain's high-low decomposition
method. As a corollary, we obtain probabilistic global existence results in
$L^2$-based Sobolev spaces. We also obtain global well-posedness in
$H^{\frac12+} \times L^2$, which is sharp (up to endpoints) in the class of
$L^2$-based Sobolev spaces. |
| doi_str_mv | 10.48550/arxiv.1805.07604 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1805_07604</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1805_07604</sourcerecordid><originalsourceid>FETCH-LOGICAL-a674-c0972a0cf0160fae4c8f3affd155b6c1f7502a1c5bb4fa9af245a789c27c09303</originalsourceid><addsrcrecordid>eNotjz1rwzAURbV0KGl_QKdq6GrnyZYsezShaQOBLp5KwTwperGpbRXZhISQ_958TXe491w4jL0IiGWuFMwx7NtdLHJQMegM5CMrSz74yXE_8G3nDXbc7dtxcoN1nHzgU-P4N_42GPyOj4dz01-2bz89To0xx-r0xB4Iu9E933PGquV7tfiM1l8fq0W5jjDTMrJQ6ATBEogMCJ20OaVItBFKmcwK0goSFFYZIwkLpEQq1HlhE31GU0hn7PV2e3Wo_0LbYzjUF5f66pL-AzFIRBk</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A note on global existence for the Zakharov system on $\mathbb{T}</title><source>arXiv.org</source><creator>Compaan, E</creator><creatorcontrib>Compaan, E</creatorcontrib><description>We show that the one-dimensional periodic Zakharov system is globally
well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is
obtained by combining the I-method with Bourgain's high-low decomposition
method. As a corollary, we obtain probabilistic global existence results in
$L^2$-based Sobolev spaces. We also obtain global well-posedness in
$H^{\frac12+} \times L^2$, which is sharp (up to endpoints) in the class of
$L^2$-based Sobolev spaces.</description><identifier>DOI: 10.48550/arxiv.1805.07604</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2018-05</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1805.07604$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1805.07604$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Compaan, E</creatorcontrib><title>A note on global existence for the Zakharov system on $\mathbb{T}</title><description>We show that the one-dimensional periodic Zakharov system is globally
well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is
obtained by combining the I-method with Bourgain's high-low decomposition
method. As a corollary, we obtain probabilistic global existence results in
$L^2$-based Sobolev spaces. We also obtain global well-posedness in
$H^{\frac12+} \times L^2$, which is sharp (up to endpoints) in the class of
$L^2$-based Sobolev spaces.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjz1rwzAURbV0KGl_QKdq6GrnyZYsezShaQOBLp5KwTwperGpbRXZhISQ_958TXe491w4jL0IiGWuFMwx7NtdLHJQMegM5CMrSz74yXE_8G3nDXbc7dtxcoN1nHzgU-P4N_42GPyOj4dz01-2bz89To0xx-r0xB4Iu9E933PGquV7tfiM1l8fq0W5jjDTMrJQ6ATBEogMCJ20OaVItBFKmcwK0goSFFYZIwkLpEQq1HlhE31GU0hn7PV2e3Wo_0LbYzjUF5f66pL-AzFIRBk</recordid><startdate>20180519</startdate><enddate>20180519</enddate><creator>Compaan, E</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180519</creationdate><title>A note on global existence for the Zakharov system on $\mathbb{T}</title><author>Compaan, E</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-c0972a0cf0160fae4c8f3affd155b6c1f7502a1c5bb4fa9af245a789c27c09303</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Compaan, E</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Compaan, E</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A note on global existence for the Zakharov system on $\mathbb{T}</atitle><date>2018-05-19</date><risdate>2018</risdate><abstract>We show that the one-dimensional periodic Zakharov system is globally
well-posed in a class of low-regularity Fourier-Lebesgue spaces. The result is
obtained by combining the I-method with Bourgain's high-low decomposition
method. As a corollary, we obtain probabilistic global existence results in
$L^2$-based Sobolev spaces. We also obtain global well-posedness in
$H^{\frac12+} \times L^2$, which is sharp (up to endpoints) in the class of
$L^2$-based Sobolev spaces.</abstract><doi>10.48550/arxiv.1805.07604</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1805.07604 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1805_07604 |
| source | arXiv.org |
| subjects | Mathematics - Analysis of PDEs |
| title | A note on global existence for the Zakharov system on $\mathbb{T} |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T09%3A26%3A29IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20note%20on%20global%20existence%20for%20the%20Zakharov%20system%20on%20$%5Cmathbb%7BT%7D&rft.au=Compaan,%20E&rft.date=2018-05-19&rft_id=info:doi/10.48550/arxiv.1805.07604&rft_dat=%3Carxiv_GOX%3E1805_07604%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |