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Publication 18-CNA-033

Fluctuations of random semi-linear advection equations

Yu Gu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA

Tomasz Komorowski
Institute of Mathematics, UMCS, pl. Marii Curie-Sklodowskiej 1, 20-031, Lublin
IMPAN, ul. Sniadeckich 8, 00-956 Warsaw, Poland

Lenya Ryzhik
Department of Mathematics
Stanford University
Stanford, CA 94305

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 random diffeomorphism, and the point-wise limiting distribution is obtained by applying the diffeomorphism to the limit in the linear setting.

Get the paper in its entirety as  18-CNA-033.pdf

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