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Proceedings of the American Mathematical Society
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A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space


Author: Luc Molinet
Journal: Proc. Amer. Math. Soc. 141 (2013), 2793-2798
MSC (2010): Primary 35Q53, 35M10
Published electronically: April 12, 2013
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Abstract: In this paper we study the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space $ H^{1/2}(\mathbb{R})$ or $ H^{1/2}(\mathbb{T}) $. We prove the strong convergence in the energy space of the solution to this equation toward the solution of the Benjamin-Ono equation as the dissipation coefficient converges to 0.


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Additional Information

Luc Molinet
Affiliation: Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais Tours, Fédération Denis Poisson-CNRS, Parc Grandmont, 37200 Tours, France
Email: luc.molinet@lmpt.univ-tours.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11693-X
PII: S 0002-9939(2013)11693-X
Keywords: Benjamin-Ono equation, inviscid limit
Received by editor(s): November 3, 2011
Published electronically: April 12, 2013
Additional Notes: The author is grateful to the Schrödinger Institute of Wien, where this work was initiated.
Communicated by: Walter Craig
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.