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On the well-posedness
of the generalized Korteweg–de Vries equation in
scale-critical $\hat{L}^r$-space
Satoshi Masaki and Jun-ichi Segata |
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Vol. 9 (2016), No. 3, 699–725
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Abstract |
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The purpose of this paper is to study local and global well-posedness of the initial value problem for the generalized Korteweg–de Vries (gKdV) equation in . We show (large-data) local well-posedness, small-data global well-posedness, and small-data scattering for the gKdV equation in the scale-critical -space. A key ingredient is a Stein–Tomas-type inequality for the Airy equation, which generalizes the usual Strichartz estimates for -framework. |
Keywords
generalized Korteweg–de Vries equation, scattering problem
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Mathematical Subject Classification 2010
Primary: 35Q53, 35B40
Secondary: 35B30
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Milestones
Received: 28 July 2015
Revised: 17 November 2015
Accepted: 30 January 2016
Published: 17 June 2016
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Authors |
| Satoshi Masaki | |
| Laboratory of Mathematics Institute of Engineering Hiroshima University Higashihiroshima, Hiroshima 739-8527 Japan |
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| Jun-ichi Segata | |
| Mathematical Institute Tohoku University 6-3, Aoba, Aramaki, Aoba-ku Sendai 980-8578 Japan |
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