{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:W7W53IA64UFOH3RRA4B54A6JUW","short_pith_number":"pith:W7W53IA6","schema_version":"1.0","canonical_sha256":"b7eddda01ee50ae3ee310703de03c9a5b46435dd348b8e7f8368cab161ff9335","source":{"kind":"arxiv","id":"1511.03808","version":2},"attestation_state":"computed","paper":{"title":"Global well-posedness and Nonsqueezing property for the higher-order KdV-type flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chulkwang Kwak, Sunghyun Hong","submitted_at":"2015-11-12T08:02:19Z","abstract_excerpt":"In this paper, we prove that the periodic higher-order KdV-type equation \\[\\left\\{\\begin{array}{ll} \\partial_t u + (-1)^{j+1} \\partial_x^{2j+1}u + \\frac12 \\partial_x(u^2)=0, \\hspace{1em} &(t,x) \\in \\mathbb{R} \\times \\mathbb{T}, \\\\ u(0,x) = u_0(x), &u_0 \\in H^s(\\mathbb{T}). \\end{array} \\right.\\] is globally well-posed in $H^s$ for $s \\ge -\\frac{j}{2}$, $j \\ge 3$. The proof of the global well-posedness is based on \"I-method\" introduced by Colliander et al. \\cite{CKSTT1}. To apply \"I-method\", we factorize the resonant functions by using the different ways from Hirayama \\cite{Hirayama}. 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The proof of the global well-posedness is based on \"I-method\" introduced by Colliander et al. \\cite{CKSTT1}. To apply \"I-method\", we factorize the resonant functions by using the different ways from Hirayama \\cite{Hirayama}. 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