On the (generalized) Korteweg-de Vries equation (Q1812879)
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scientific article; zbMATH DE number 4569
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the (generalized) Korteweg-de Vries equation |
scientific article; zbMATH DE number 4569 |
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On the (generalized) Korteweg-de Vries equation (English)
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25 June 1992
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The well-posedness of the initial value problem for the Korteweg-de Vries equation \(u_ t+ u_{xxx}+ uu_ x =0\) and its generalized form \(u_ t+ u_{xxx}+ a(u) u_ x=0\) in the classical Sobolev spaces and the regularity of their solutions in \(L_ s^ p\) spaces are studied. A global smoothing effect of the solutions of these equations is also proved. See also a paper by \textit{T. Kato} [Studies in applied mathematics, Adv. Math., Suppl. Stud., Vol. 8, 93-128 (1983; Zbl 0508.00010)].
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well-posedness
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initial value problem
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Korteweg-de Vries equation
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Sobolev spaces
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regularity
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global smoothing
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