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

TL;DR

This paper investigates the behavior of solutions to the Benjamin-Ono-Burgers equation as dissipation vanishes, proving strong convergence to the Benjamin-Ono equation's solutions in the energy space.

Contribution

It establishes the strong convergence of solutions in the energy space for the inviscid limit of the Benjamin-Ono-Burgers equation, a result not previously shown.

Findings

Solutions converge strongly in the energy space as dissipation tends to zero

The convergence holds in both real line and torus settings

Provides rigorous mathematical proof of the inviscid limit behavior

Abstract

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