Min-Max Variational Principle and Front Speeds in Random Shear Flows

2005/01/25 by James Nolen, Jack Xin, Nolen, James +1
Engineering · Environmental Science · Mathematics · Physics and Astronomy · #35K57 #41A60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Hydrology and Sediment Transport Processes #Model Reduction and Neural Networks #Probability (math.PR) #math.AP #math.PR #msc:35K57 #msc:41A60

paper · pdf · doi:10.48550/arxiv.math/0501445

15 pages, no figures

arxiv created 2005/01/25 · openalex publication_date 2005/01/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Speed ensemble of bistable (combustion) fronts in mean zero stationary Gaussian shear flows inside two and three dimensional channels is studied with a min-max variational principle. In the small root mean square regime of shear flows, a new class of multi-scale test functions are found to yield speed asymptotics. The quadratic speed enhancement law holds with probability arbitrarily close to one under the almost sure continuity (dimension two) and mean square Hölder regularity (dimension three) of the shear flows. Remarks are made on the conditions for the linear growth of front speed expectation in the large root mean square regime.

Citations

• Variational Principles for Propagation Speeds in Inhomogeneous Media

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