Periodic homogenization of the inviscid G-equation for incompressible flows

Jack Xin Yifeng Yu

Analysis of PDEs mathscidoc:1912.43848

Communications in Mathematical Sciences, 8, (4), 1067-1078, 2010
G-equations are popular front propagation models in combustion literature and describe the front motion law of normal velocity equal to a constant plus the normal projection of fluid velocity. G-equations are Hamilton-Jacobi equations with convex but non-coercive Hamiltonians. We prove homogenization of the inviscid G-equation for space periodic incompressible flows. This extends a two space dimensional result in" Periodic homogenization of G-equations and viscosity effects," Nonlinearity, to appear. We construct approximate correctors to bypass the lack of compactness due to the non-coercive Hamiltonian. The existence of approximate correctors rely on a local reachability property of the controlled flow trajectory as well as incompressibility of the flow. Homogenization then follows from the comparison principle and the perturbed test function method. The effective Hamiltonian is convex and homogeneous of
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@inproceedings{jack2010periodic,
  title={Periodic homogenization of the inviscid G-equation for incompressible flows},
  author={Jack Xin, and Yifeng Yu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210156534096412},
  booktitle={Communications in Mathematical Sciences},
  volume={8},
  number={4},
  pages={1067-1078},
  year={2010},
}
Jack Xin, and Yifeng Yu. Periodic homogenization of the inviscid G-equation for incompressible flows. 2010. Vol. 8. In Communications in Mathematical Sciences. pp.1067-1078. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210156534096412.
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