Advances in Differential Equations

Local well-posedness for the KdV hierarchy at high regularity

Carlos E. Kenig and Didier Pilod

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We prove well-posedness in $L^2$-based Sobolev spaces $H^s$ at high regularity for a class of nonlinear higher-order dispersive equations generalizing the KdV hierarchy both on the line and on the torus.

Article information

Adv. Differential Equations, Volume 21, Number 9/10 (2016), 801-836.

First available in Project Euclid: 14 June 2016

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Zentralblatt MATH identifier

Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 37K10: Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.) 35A01: Existence problems: global existence, local existence, non-existence 37K05: Hamiltonian structures, symmetries, variational principles, conservation laws 35E15: Initial value problems


Kenig, Carlos E.; Pilod, Didier. Local well-posedness for the KdV hierarchy at high regularity. Adv. Differential Equations 21 (2016), no. 9/10, 801--836.

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