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

James Nolen, Alexei Novikov

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)561-582
Number of pages22
JournalCommunications in Mathematical Sciences
Volume9
Issue number2
DOIs
StatePublished - Jun 2011

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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