Ill-posedness results for the (generalized) Benjamin-Ono-Zakharov-Kuznetsov equation
نویسندگان
چکیده
منابع مشابه
Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation
We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation ut −D α xux + uxyy = uux, (t, x, y) ∈ R , 1 ≤ α ≤ 2, is locally well-posed in the spaces Es, s > 2 α − 3 4 , endowed with the norm ‖f‖Es = ‖〈|ξ| α + μ〉f̂‖L2(R2). As a consequence, we get the global wellposedness in the energy space E1/2 as soon as α > 8 5 . The proof is based ...
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This paper studies the generalized version of theZakharov-Kuznetsov Benjamin-Bona-Mahoney equation. The functionalvariable method as well as the simplest equation method areapplied to obtain solitons and singular periodic solutions to theequation. There are several constraint conditions that arenaturally revealed in order for these specialized type ofsolutions to exist. The results of this pape...
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We establish the local well-posedness of the generalized BenjaminOno equation ∂tu+H∂ xu±u ∂xu = 0 in Hs(R), s > 1/2−1/k for k ≥ 12 and without smallness assumption on the initial data. The condition s > 1/2−1/k is known to be sharp since the solution map u0 7→ u is not of class Ck+1 on Hs(R) for s < 1/2 − 1/k. On the other hand, in the particular case of the cubic Benjamin-Ono equation, we prov...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10532-4