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2016•Unpublished venueRequires access

WELL-POSEDNESS AND ILL-POSEDNESS RESULTS FOR THE REGULARIZED BENJAMIN-ONO EQUATION IN WEIGHTED SOBOLEV SPACES

Guillermo Rodrguez-blanco, Wilson Sandoval

Open publisher page 8 citations

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 Sobolevspaces 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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What this paper is about

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 Sobolevspaces 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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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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 Sobolevspaces 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.

Key concepts: Sobolev space, Mathematics, Continuation, Initial value problem, Well-posed problem, Contraction (grammar), Mathematical analysis, Property (philosophy)

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WELL-POSEDNESS AND ILL-POSEDNESS RESULTS FOR THE REGULARIZED BENJAMIN-ONO EQUATION IN WEIGHTED SOBOLEV SPACES — Research Paper | ScholarLens