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Well-Posedness for the ZK Equation in a Cylinder and on the Background of a KdV Soliton

2010; Taylor & Francis; Volume: 35; Issue: 9 Linguagem: Inglês

10.1080/03605302.2010.494195

ISSN

1532-4133

Autores

Felipe Linares, Ademir Pastor, Jean‐Claude Saut,

Tópico(s)

Navier-Stokes equation solutions

Resumo

Abstract We establish the well-posedness of two Cauchy problems for the two-dimensional Zakharov–Kuznetsov equation motivated by the study of transverse stability properties of the N-soliton φ N of the Korteweg–de Vries equation. They differ by the functional setting: Sobolev spaces H s (ℝ × 𝕋), for the first one, φ N + H 1(ℝ2) for the second one. In the latter case, the solution is shown to be global. Keywords: KdV N-solitonsStrichartz estimatesWell-posednessMathematics Subject Classification: Primary 35Q53, 35B10Secondary 35Q60 Acknowledgments The authors acknowledge support from the Brazilian-French Program for Mathematics. F. L. was partially supported by CNPq-Brazil, A. P. was supported by CNPq-Brazil under grant 152234/2007-1 and J.-C. S. was partially supported by the project ANR-07-BLAN-0250 of the Agence Nationale de la Recherche and by the Wolfgang Pauli Institute in Vienna. A. P. is currently at IMECC-UNICAMP, Rua Sérgio Buarque de Holanda 651, 13083-859, Campinas, SP, Brazil.

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