Probabilistic well-posedness of generalized KdV

Hwang, Gyeongha; Kwak, Chulkwang

doi:10.1090/proc/13718

Probabilistic well-posedness of generalized KdV
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by Gyeongha Hwang and Chulkwang Kwak PDF

Proc. Amer. Math. Soc. 146 (2018), 267-280 Request permission

Abstract:

We consider the Cauchy problem of the generalized Korteweg-de Vries (gKdV) equation. We prove the local well-posedness of the mass supercritical gKdV equations for the scaling supercritical regularity $s < s_c = \frac 12 - \frac 2\kappa$ in the sense of the probabilistic manner. The main ingredient is to establish the probabilistic local smoothing estimate.

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