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Mathematics - Dynamical Systems & Differential Equations | Burgers-KPZ Turbulence - Göttingen Lectures

Burgers-KPZ Turbulence

Göttingen Lectures

Series: Lecture Notes in Mathematics, Vol. 1700

Woyczynski, Wojbor A.

1998, XII, 328 p.

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  • About this book

These lecture notes are woven around the subject of Burgers' turbulence/KPZ model of interface growth, a study of the nonlinear parabolic equation with random initial data. The analysis is conducted mostly in the space-time domain, with less attention paid to the frequency-domain picture. However, the bibliography contains a more complete information about other directions in the field which over the last decade enjoyed a vigorous expansion. The notes are addressed to a diverse audience, including mathematicians, statisticians, physicists, fluid dynamicists and engineers, and contain both rigorous and heuristic arguments. Because of the multidisciplinary audience, the notes also include a concise exposition of some classical topics in probability theory, such as Brownian motion, Wiener polynomial chaos, etc.

Content Level » Research

Keywords » Brownian motion - Burgers turbulence - KPZ moxdel - Probability theory - nonlinear difffusions - polynomial chaos - random fields - shock waves

Related subjects » Dynamical Systems & Differential Equations - Probability Theory and Stochastic Processes

Table of contents 

Shock waves and the large scale structure (LSS) of the universe.- Hydrodynamic limits, nonlinear diffusions, and propagation of chaos.- Hopf-Cole formula and its asymptotic analysis.- Statistical description, parabolic approximation.- Hyperbolic approximation and inviscid limit.- Forced Burgers turbulence.- Passive tracer transport in Burgers' and related flows.- Fractal Burgers-KPZ models.

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