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Zbl 0795.35105
Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis
On the (generalized) Korteweg-de Vries equation.
(English)
[J] Duke Math. J. 59, No.3, 585-610 (1989). ISSN 0012-7094

The well-posedness of the initial value problem for the Korteweg-de Vries equation $u\sb t+ u\sb{xxx}+ uu\sb x =0$ and its generalized form $u\sb t+ u\sb{xxx}+ a(u) u\sb x=0$ in the classical Sobolev spaces and the regularity of their solutions in $L\sb s\sp p$ spaces are studied. A global smoothing effect of the solutions of these equations is also proved. See also a paper by {\it T. Kato} [Studies in applied mathematics, Adv. Math., Suppl. Stud., Vol. 8, 93-128 (1983; Zbl 0508.00010)].
MSC 2000:
*35Q53 KdV-like equations
35B65 Smoothness of solutions of PDE

Keywords: well-posedness; initial value problem; Korteweg-de Vries equation; Sobolev spaces; regularity; global smoothing

Citations: Zbl 0508.00010

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