Well-posedness of the Cauchy problem for the Korteweg-de Vries equation at the critical regularity

By Nobu Kishimoto. Differential and Integral Equations, 2009

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Global well-posedness of Korteweg-de Vries equation in H^-3/4 (R) (2008, result): “deas in [7] to prove the inviscid limit in C([−T,T] : H−3/4) as ǫtends to zero. We do not pursue this in this paper. Remark 1.3. After this paper was published, the author learned that Nobu Kishimoto [16] also obtained similar results with diﬀerent resolution spaces by using some ideas in [1]. The a”
Lower Bounds on the Radius of Spatial Analyticity for the KdV Equation (2015, unknown): “It is by now known that local well-posedness holds in H for s ≥ −3/4 (see [4,14]) and that for s < −3/4, there is ill-posedness (see [4,15,18]).”
Global well-posedness of the one-dimensional cubic nonlinear Schrödinger equation in almost critical spaces (2018, unknown): “2) in Hs(M) for s ≥ 1 4 on the real line and for s ≥ 12 on the circle [17, 35].”
Long time behavior of solutions to the mKdV (2014, background): “In particular, the mKdV is both locally well-posed [22–24] and globally well-posed [3, 11, 26] in H for s ≥ 1 4 .”
KdV is well-posed in H–1 (2018, background): “These local well-posedness results were made global in time in [12], excepting the endpoint case H−3/4(R), which was proved later in [21, 34].”