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arXiv · 1802.00302

Fluctuations of random semi-linear advection equations

Yu Gu·Tomasz Komorowski·Lenya Ryzhik
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Abstract

We consider a semi-linear advection equation driven by a highly-oscillatory space-time Gaussian random field, with the randomness affecting both the drift and the nonlinearity. In the linear setting, classical results show that the characteristics converge in distribution to a homogenized Brownian motion, hence the point-wise law of the solution is close to a functional of the Brownian motion. Our main result is that the nonlinearity plays the role of a \emph{random diffeomorphism}, and the point-wise limiting distribution is obtained by applying the diffeomorphism to the limit in the linear setting.

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Yu Gu, Tomasz Komorowski, Lenya Ryzhik. 2018-02-01. Fluctuations of random semi-linear advection equations. https://arxiv.org/abs/1802.00302

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