A symplectic non-squeezing theorem for BBM equation
We study the initial value problem for the BBM equation: $$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on $H^{1/2}(\...
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| creator | Roumegoux, David |
| description | We study the initial value problem for the BBM equation:
$$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R
u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly
well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on
$H^{1/2}(\T)$. That is to say the flow-map $u_0 \mapsto u(t)$ that associates
to initial data $u_0 \in H^{1/2}(\T)$ the solution $u$ cannot send a ball into
a symplectic cylinder of smaller width. |
| doi_str_mv | 10.48550/arxiv.1007.1359 |
| format | Article |
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$$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R
u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly
well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on
$H^{1/2}(\T)$. That is to say the flow-map $u_0 \mapsto u(t)$ that associates
to initial data $u_0 \in H^{1/2}(\T)$ the solution $u$ cannot send a ball into
a symplectic cylinder of smaller width.</description><identifier>DOI: 10.48550/arxiv.1007.1359</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2010-07</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/1007.1359$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1007.1359$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Roumegoux, David</creatorcontrib><title>A symplectic non-squeezing theorem for BBM equation</title><description>We study the initial value problem for the BBM equation:
$$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R
u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly
well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on
$H^{1/2}(\T)$. That is to say the flow-map $u_0 \mapsto u(t)$ that associates
to initial data $u_0 \in H^{1/2}(\T)$ the solution $u$ cannot send a ball into
a symplectic cylinder of smaller width.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrFuwjAQgGEvHRBlZ6r8AkntXM92RkAtrQRiYY8O59xaIgk4oQKevqIw_duvT4ipVvmbQ1SvlM7xN9dK2VwDliMBM9lfmsOe_RC9bLs2648n5mtsv-Xww13iRoYuyfl8Lfl4oiF27bN4CrTvefLoWGw_3reLz2y1WX4tZquMDJYZWjCMvmYINrhQaq8dKGMVFoFqMOiMJvbWBGutI_BhZwosaqN2pEsoYCxe7tt_dHVIsaF0qW746oaHP3r-Pgc</recordid><startdate>20100708</startdate><enddate>20100708</enddate><creator>Roumegoux, David</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20100708</creationdate><title>A symplectic non-squeezing theorem for BBM equation</title><author>Roumegoux, David</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a659-5736e5cde3f7f8f91c183067052fad365861aec76f7778a3cfb6252d60ba19323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Roumegoux, David</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Roumegoux, David</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A symplectic non-squeezing theorem for BBM equation</atitle><date>2010-07-08</date><risdate>2010</risdate><abstract>We study the initial value problem for the BBM equation:
$$\left\{\begin{array}{l} u_t+u_x+uu_x-u_{txx}=0 \qquad x\in \T, t \in \R
u(0,x)=u_0(x) \end{array} \right. .$$ We prove that the BBM equation is globaly
well-posed on $H^s(\T)$ for $s\geq0$ and a symplectic non-squeezing theorem on
$H^{1/2}(\T)$. That is to say the flow-map $u_0 \mapsto u(t)$ that associates
to initial data $u_0 \in H^{1/2}(\T)$ the solution $u$ cannot send a ball into
a symplectic cylinder of smaller width.</abstract><doi>10.48550/arxiv.1007.1359</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Mathematics - Analysis of PDEs |
| title | A symplectic non-squeezing theorem for BBM equation |
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