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Min-max variational principle and front speeds in random shear flows

James Nolen Jack Xin

Analysis of PDEs mathscidoc:1912.43881

Methods and Applications of Analysis, 11, (4), 635-644, 2004
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 Hlder regularity (dimension three) of the shear flows. Remarks are made on the quadratic and linear laws of front speed expectation in the small and large root mean square regimes.
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@inproceedings{james2004min-max,
  title={Min-max variational principle and front speeds in random shear flows},
  author={James Nolen, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210422102506445},
  booktitle={Methods and Applications of Analysis},
  volume={11},
  number={4},
  pages={635-644},
  year={2004},
}
James Nolen, and Jack Xin. Min-max variational principle and front speeds in random shear flows. 2004. Vol. 11. In Methods and Applications of Analysis. pp.635-644. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210422102506445.
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