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Large-Scale Structure of the Universe and Asymptotics of Burgers' Turbulence with Heavy-tailed Dependent Data Yiming Hue and

  • W. A. Woyczynskil
  • Yiming Hu
Part I: Lectures
Part of the Lecture Notes in Physics book series (LNP, volume 457)

Abstract

Large-time asymptotics of the statistical solutionsν(t,χ) of the Burgers' equation ν t + ννχ = ννχχ is considered. The initial velocity potential is assumed to be of the shot noise type with dependent amplitudes and heavy tails. The problem arises naturally in the adhesion model of the large-scale distribution of matter in the Universe. As t → ∞, the random field ν(t, χ) becomes stochastically relatively asymptotically equivalent to a field with “saw-tooth” trajectories. The intermittent shocks of the velocity field correspond then to the regions of high density in the coupled passive tracer density field. This paper extends a result of S.Albeverio, S.A.Molchanov and D. Surgailis (1992), obtained for the case of independent amplitudes.

Keywords

Random Field Shot Noise Burger Equation Heavy Tail Dependent Amplitude 
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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • W. A. Woyczynskil
    • 1
    • 2
  • Yiming Hu
    • 2
  1. 1.Department of StatisticsCase Western Reserve UniversityCleveland
  2. 2.Center for Stochastic and Chaotic Processes in Science and TechnologyCase Western Reserve UniversityCleveland

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