Remarks on the two-dimensional Benjamin equation

Ibtissame Zaiter (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Physique mathématique [math-ph]

Ibtissame Zaiter. Remarks on the two-dimensional Benjamin equation. Applied Mathematics Letters, 2009, 22 (7), pp.1102--1106. ⟨10.1016/j.aml.2008.11.003⟩. ⟨hal-00693131⟩