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

G. Fonseca; G. Rodríguez-Blanco; W. Sandoval

doi:10.3934/cpaa.2015.14.1327

Article Contents

2015, Volume 14, Issue 4: 1327-1341. Doi: 10.3934/cpaa.2015.14.1327

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

1.
Universidad Nacional de Colombia, Bogotá

Received: April 30, 2013

Revised: August 31, 2013

Published: June 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 35B05; Secondary: 35B60.

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