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 (Formula Presented) in the sense of the probabilistic manner. The main ingredient is to establish the probabilistic local smoothing estimate.
| Original language | English |
|---|---|
| Pages (from-to) | 267-280 |
| Number of pages | 14 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 146 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2017 American Mathematical Society.
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