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 $.
Well-posedness and scattering for NLS on $\R^d\times \T $ in the energy space
Stability in the energy space of the sum of N peakons for the Degasperis-Procesi equation
Kink dynamics in the $φ^4$ model: asymptotic stability for odd perturbations in the energy space
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