Burgers equation with self-similar gaussian initial data: Tail probabilities

Details Burgers equation with self-similar gaussian initial data: Tail probabilities Burgers equation with self-similar gaussian initial data: Tail probabilities

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996jsp....88.1139m&link_type=abstract

Journal of Statistical Physics, Volume 88, Issue 5-6, pp. 1139-1150

Physics

13

Burgers Equation, Fractional Brownian Motion, Tail Probabilities

Scientific paper

The statistical properties of solutions of the one-dimensional Burgers equation in the limit of vanishing viscosity are considered when the initial velocity potential is fractional Brownian motion (FBM). We establish the asymptotic power-law order for log-probability of large values, both velocity and shock (amplitude of velocity discontinuity). This confirms the conjecture of U. Frisch and his collaborators. Rigorous results for this problem were previously derived for the case of Brownian motion using Markov techniques. Our approach is based on the intrinsic properties of FBM and the theory of extreme values for Gaussian processes.

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