On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics

Neate, Andrew and Truman, Aubrey (2008). On the Stochastic Burgers Equation and Some Applications to Turbulence and Astrophysics. In: Morters, Peter; Moser, Roger; Penrose, Mathew; Schwetlick, Hartmut and Zimmer, Johannes eds. Analysis and Stochastics of Growth Processes and Interface Models. Oxford: Oxford University Press, pp. 281–305.

DOI: https://doi.org/10.1093/acprof:oso/9780199239252.003.0013

Abstract

This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.

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