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July  2015, 14(4): 1327-1341. doi: 10.3934/cpaa.2015.14.1327

## Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces

 1 Universidad Nacional de Colombia, Bogotá, Colombia, Colombia, Colombia

Received  May 2013 Revised  September 2013 Published  April 2015

We consider the initial value problem associated to the regularized Benjamin-Ono equation, rBO. Our aim is to establish local and global well-posedness results in weighted Sobolev spaces via contraction principle. We also prove a unique continuation property that implies that arbitrary polynomial type decay is not preserved yielding sharp results regarding well-posedness of the initial value problem in most weighted Sobolev spaces.
Citation: G. Fonseca, G. Rodríguez-Blanco, W. Sandoval. Well-posedness and ill-posedness results for the regularized Benjamin-Ono equation in weighted Sobolev spaces. Communications on Pure & Applied Analysis, 2015, 14 (4) : 1327-1341. doi: 10.3934/cpaa.2015.14.1327
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