Author | Woyczyล{132}ski, Wojbor A. author |
---|---|

Title | Burgers-KPZ Turbulence [electronic resource] : Gรถttingen Lectures / by Wojbor A. Woyczyล{132}ski |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1998 |

Connect to | http://dx.doi.org/10.1007/BFb0093107 |

Descript | XII, 328 p. online resource |

SUMMARY

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

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

Mathematics
Partial differential equations
Probabilities
Mathematics
Partial Differential Equations
Probability Theory and Stochastic Processes