Burgers-KPZ turbulence

Description:

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.

subjects: Burgers equation,  Differential equations, Parabolic,  Interfaces (Physical sciences),  Mathematical models,  Parabolic Differential equations,  Turbulence,  Mathematics,  Distribution (Probability theory),  Partial Differential equations,  Fractales,  Equation de Burgers,  Burgers-Gleichung,  Equations differentielles paraboliques,  Equacoes diferenciais parciais,  Stochastische analyse,  Interfaces (sciences physiques),  Modeles mathematiques,  Mecanica e dinamica dos fluidos,  Turbulenz,  KPZ-Gleichung,  Ondes de choc,  Differential equations, partial