On the periodic Korteweg-de Vries equation: a normal form approach
This paper discusses an improved smoothing phenomena for low-regularity solutions of the Korteweg-de Vries (KdV) equation in the periodic settings by means of normal form transformation. As a result, the solution map from a ball on $H^{-1/2+}$ to $C_0^t ([0,T], H^{-1/2+})$ can be shown to be Lipschi...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
10.08.2011
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| Subjects | |
| Online Access | Get full text |
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| Summary: | This paper discusses an improved smoothing phenomena for low-regularity
solutions of the Korteweg-de Vries (KdV) equation in the periodic settings by
means of normal form transformation. As a result, the solution map from a ball
on $H^{-1/2+}$ to $C_0^t ([0,T], H^{-1/2+})$ can be shown to be Lipschitz in a
$H^{0+}_x$ topology, where the Lipschitz constant only depends on the rough
norm $\|u_0\|_{H^{-1/2+}}$ of the initial data. A similar episode has been
observed in a recent paper on 1D quadratic Schr\"odinger equation in
low-regularity setting. |
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| DOI: | 10.48550/arxiv.1108.2249 |