The low-dispersion fractional KdV equation is unconditionally globally well-posed in L2(R) for alpha in (55/38, 2].
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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].