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arXiv · 1802.02356

On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise

Romain Duboscq
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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 $\in$ (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.

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Romain Duboscq. 2018-02-07. On Strichartz estimates for a dispersion modulated by a time-dependent deterministic noise. https://arxiv.org/abs/1802.02356

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