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

Research paper by G. Molchan

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematical Physics

#### 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.