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

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


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