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arXiv · 2209.14116

Refined probabilistic local well-posedness for a cubic Schr\"odinger half-wave equation

Nicolas Camps·Louise Gassot·Slim Ibrahim
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Abstract

We obtain probabilistic local well-posedness in quasilinear regimes for the Schr\"odinger half-wave equation with a cubic nonlinearity. We need to use a refined ansatz because of the lack of probabilistic smoothing in the Picard's iterations, which is due to the high-low-low frequency interactions. The proof is an adaptation of the method of Bringmann on the derivative nonlinear wave equation to Schr\"odinger-type equations. In addition, we discuss ill-posedness results for this equation.

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Nicolas Camps, Louise Gassot, Slim Ibrahim. 2022-09-28. Refined probabilistic local well-posedness for a cubic Schr\"odinger half-wave equation. https://arxiv.org/abs/2209.14116

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