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- W2066884096 abstract "In this Note we study the generalized 2D Zakharov–Kuznetsov equations ∂tu+Δ∂xu+uk∂xu=0 for k⩾2. By an iterative method we prove the local well-posedness of these equations in the Sobolev spaces Hs(R2) for s>1/4 if k=2, s>5/12 if k=3 and s>1−2/k if k⩾4. Nous étudions dans cette Note les équations de Zakharov–Kuznetsov 2D généralisées ∂tu+Δ∂xu+uk∂xu=0 pour k⩾2. Il est établi que le problème de Cauchy peut être résolu par une méthode itérative dans les espaces de Sobolev Hs(R2) pour s>1/4 si k=2, s>5/12 si k=3 et s>1−2/k si k⩾4." @default.
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- W2066884096 date "2012-05-01" @default.
- W2066884096 modified "2023-10-14" @default.
- W2066884096 title "A Note on the Cauchy problem for the 2D generalized Zakharov–Kuznetsov equations" @default.
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- W2066884096 doi "https://doi.org/10.1016/j.crma.2012.05.007" @default.
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