On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise
Analysis of PDEs
2018-02-08 v1
Abstract
We address the Cauchy problem for a nonlinear Schr{\"o}dinger equation where the dispersion is modulated by a deterministic noise. The noise is understood as the derivative of a self-affine function of order H (0, 1). Due to the self-similarity of the noise, we obtain modified Strichartz estimates which enables us to prove the global well-posedness of the equation for L2-supercritical nonlinearities. This is an occurence of regularization by noise in a purely deterministic context.
Keywords
Cite
@article{arxiv.1802.02356,
title = {On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise},
author = {Romain Duboscq},
journal= {arXiv preprint arXiv:1802.02356},
year = {2018}
}