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Remarks on the two-dimensional Benjamin equation

Abstract : We generalize some recent results proved for the KP equation to the generalized Benjamin equation. First, we establish that the Cauchy problem cannot be solved by an iteration method. As a consequence, the flow map fails to be smooth. The second goal is to prove that the zero-mass constraint is satisfied at any non-zero time even it is not satisfied at the initial time. (C) 2009 Elsevier Ltd. All rights reserved.
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Ibtissame Zaiter. Remarks on the two-dimensional Benjamin equation. Applied Mathematics Letters, Elsevier, 2009, 22 (7), pp.1102--1106. ⟨10.1016/j.aml.2008.11.003⟩. ⟨hal-00693131⟩



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