Homogenization of the G-equation with incompressible random drift in two dimensions

Journal Article

We study the homogenization limit of solutions to the G-equation with random drift. This Hamilton-Jacobi equation is a model for flame propagation in a turbulent fluid in the regime of thin flames. For a fluid velocity field that is statistically stationary and ergodic, we prove sufficient conditions for homogenization to hold with probability one. These conditions are expressed in terms of travel times for the associated control problem. When the spatial dimension is equal to two and the fluid velocity is divergence-free, we verify that these conditions hold under suitable assumptions about the growth of the random stream function. © 2011 International Press.

Full Text

Duke Authors

Cited Authors

  • Nolen, J; Novikov, A

Published Date

  • January 1, 2011

Published In

Volume / Issue

  • 9 / 2

Start / End Page

  • 561 - 582

International Standard Serial Number (ISSN)

  • 1539-6746

Digital Object Identifier (DOI)

  • 10.4310/CMS.2011.v9.n2.a11

Citation Source

  • Scopus