The inviscid Burgers equation with fractional Brownian initial data: the dimension of regular Lagrangian points

Abstract

Fractional Brownian motion, H-FBM , of index 0<H<1 is considered as initial velocity in the inviscid Burgers equation. It is shown that the Hausdorff dimension of regular Lagrangian points at any moment t is equal to H. This fact validates the Sinai-Frisch conjecture known since 1992.

7 pages

Cited by in corpus (3)

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• Asymptotics of the persistence exponent of integrated fractional Brownian motion and fractionally integrated Brownian motion
• Persistence probabilities of mixed FBM and other mixed processes