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

In this paper we study the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space $H^{1\mathrm{/}2}(\mathbb{R})$ or $H^{1\mathrm{/}2}(\text{T})$. 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 $0$.