A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space

Molinet, Luc

doi:10.1090/S0002-9939-2013-11693-X

A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space
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Proc. Amer. Math. Soc. 141 (2013), 2793-2798 Request permission

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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