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

作者：Linares Felipe^*; Pastor Ademir; Saut Jean Claude

来源：Communications in Partial Differential Equations, 2010, 35(9): 1674-1689.

DOI：10.1080/03605302.2010.494195

• KdV N-solitons
• Strichartz estimates
• Well-posedness

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 phi N of the Korteweg-de Vries equation. They differ by the functional setting: Sobolev spaces Hs(x), [image omitted] for the first one, phi N+H1(2) for the second one. In the latter case, the solution is shown to be global.

• 出版日期2010