The regularized Benjamin-Ono and BBM equations: Well-posedness and nonlinear stability |
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Authors: | Jaime Angulo,Má rcia Scialom |
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Affiliation: | a Department of Mathematics, IME-USP, Rua do Matão 1010, Cidade Universitária, CEP 05508-090, São Paulo, SP, Brazil b Department of Mathematics, IMECC-UNICAMP, Rua Sérgio Buarque de Holanda 651, CEP 13081-970, Campinas, SP, Brazil |
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Abstract: | 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. |
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Keywords: | 35Q53 35B35 35B10 |
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