### 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 language | English (US) |
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Pages (from-to) | 561-582 |

Number of pages | 22 |

Journal | Communications in Mathematical Sciences |

Volume | 9 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Communications in Mathematical Sciences*, vol. 9, no. 2, pp. 561-582. https://doi.org/10.4310/CMS.2011.v9.n2.a11

**Homogenization of the G-equation with incompressible random drift in two dimensions.** / Nolen, James; Novikov, Alexei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Homogenization of the G-equation with incompressible random drift in two dimensions

AU - Nolen, James

AU - Novikov, Alexei

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78650467507&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650467507&partnerID=8YFLogxK

U2 - 10.4310/CMS.2011.v9.n2.a11

DO - 10.4310/CMS.2011.v9.n2.a11

M3 - Article

VL - 9

SP - 561

EP - 582

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

SN - 1539-6746

IS - 2

ER -