Global well-posedness for the periodic ILW equation is established for all Sobolev regularities s > -1/2, together with convergence to Benjamin-Ono in the infinite-depth limit.
Baldi, Periodic solutions of fully nonlinear autonomous equations of Benjamin-Ono type , Ann
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Global well-posedness for the ILW equation in $H^s(\mathbb{T})$ for $s>-\frac12$
Global well-posedness for the periodic ILW equation is established for all Sobolev regularities s > -1/2, together with convergence to Benjamin-Ono in the infinite-depth limit.