期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 250, 期 11, 页码 4011-4036出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2010.12.016
关键词
Periodic traveling waves; Nonlinear stability; Regularized Benjamin-Ono equation; BBM equation
类别
资金
- CNPq/Brazil [14/2009]
- CNPq/Brazil at State University of Campinas
- University of Cordoba, Monteria, Colombia
Nonlinear stability of nonlinear periodic solutions of the regularized Benjamin-Ono equation and the Benjamin-Bona-Mahony equation with respect to perturbations of the same wavelength is analytically studied. These perturbations are shown to be stable. We also develop a global well-posedness theory for the regularized Benjamin-Ono equation in the periodic and in the line setting. In particular, we show that the Cauchy problem (in both periodic and nonperiodic case) cannot be solved by an iteration scheme based on the Duhamel formula for negative Sobolev indices. (C) 2010 Elsevier Inc. All rights reserved.
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