Concave Majorant of Stochastic Processes and Burgers Turbulence

Concave majorant of stochastic processes and structure of shocks in Burgers turbulence

In this paper, we study the least concave majorant of a stochastic process, and more precisely the set of times where its slope varies, which we call the extremal superior times. We establish the negligibility of this set, namely the extremal superior set, for certain classes of processes, including Lévy processes, their integrated processes, and Itô processes. We examine more closely the case ...

The Concave Majorant of Brownian Motion

Intermittency of Burgers’ Turbulence

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For the PDFs of velocity and...

Burgers Turbulence and Dynamical Systems

random burgers equation, random Hamilton-Jacobi equation, uniqueness of global minimizers We discuss a dynamical system approach to a problem of Burgers turbulence. It is shown that there exists a unique stationary distribution for solutions to spatially periodic inviscid random forced Burgers equation in arbitrary dimension. The construction is based on analysis of minimizing orbits for time-d...

Kicked Burgers Turbulence

1 Observatoire de la Côte d’Azur, Lab. G.D. Cassini, B.P. 4229, F-06304 Nice Cedex 4, France. E-mail: [email protected] 2 Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK. E-mail: [email protected] 3 Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK. 4 Landau Institute for Theoretical Physics, Kosygina Str., 2, Moscow 117332, Rus...