The low-dispersion fractional KdV equation is unconditionally globally well-posed in L2(R) for alpha in (55/38, 2].
Ginibre,Le probl` eme de Cauchy pour des EDP semi-lin´ eaires p´ eriodiques en variables d’espace (d’apr` es Bourgain),Ast´ erisque,237(1996), 163–187
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$L^2({\mathbb R}) $-Unconditional well-posedness for low dispersion fractional KdV equations
The low-dispersion fractional KdV equation is unconditionally globally well-posed in L2(R) for alpha in (55/38, 2].