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

Luc Molinet (1)

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

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 $.

Mots clés: Benjamin-Ono equation; inviscid limit

Domaines: Equations aux dérivées partielles [math.AP]

Luc Molinet. A note on the inviscid limit of the Benjamin-Ono-Burgers equation in the energy space. Proceedings of the American Mathematical Society, 2013, 141 (8), pp.2793-2798. ⟨hal-00631034⟩