Classification: 70H20, 76M50, 76M45, 76N20

Keywords: Inviscid Hamilton–Jacobi equations, Cellular flows, Sharp front speed asymptotics

@article{AIHPC_2013__30_6_1049_0, author = {Xin, Jack and Yu, Yifeng}, title = {Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton--Jacobi models}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, publisher = {Elsevier}, volume = {30}, number = {6}, year = {2013}, pages = {1049-1068}, doi = {10.1016/j.anihpc.2012.11.004}, zbl = {06286079}, mrnumber = {3132416}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2013__30_6_1049_0} }

Xin, Jack; Yu, Yifeng. Sharp asymptotic growth laws of turbulent flame speeds in cellular flows by inviscid Hamilton–Jacobi models. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, pp. 1049-1068. doi : 10.1016/j.anihpc.2012.11.004. http://www.numdam.org/item/AIHPC_2013__30_6_1049_0/

[1] Front speed enhancement in cellular flows, Chaos 12 (2002), 481-488 | MR 1907659 | Zbl 1080.80501

, , , ,[2] Réaction diffusion en écoulement stationnaire rapide, C. R. Acad. Sci. Paris 328 no. IIb (2000), 255-262

, , ,[3] Front propagation in periodic excitable media, Comm. Pure Appl. Math. 60 (2002), 949-1032 | MR 1900178 | Zbl 1024.37054

, ,[4] Homogenization and enhancement for the G-equation, Arch. Ration. Mech. Anal. 199 no. 2 (2011), 527-561 | MR 2763033 | Zbl 1294.35002

, , ,[5] P. Cardaliaguet, P.E. Souganidis, Homogenization and enhancement the G-equation in random environments, Comm. Pure Appl. Math., in press. | MR 3084699

[6] Scalar transport and alpha-effect for a family of catʼs-eye flows, J. Fluid Mech. 205 (1989), 99-133 | MR 1014361 | Zbl 0675.76091

, ,[7] Theory of premixed-flame propagation in large-scale turbulence, J. Fluid Mech. 90 (1979), 598-604 | Zbl 0434.76052

, ,[8] Bulk burning rate in passive–reactive diffusion, Arch. Ration. Mech. Anal. 154 (2000), 53-91 | MR 1778121 | Zbl 0979.76093

, , , ,[9] Convection enhanced diffusion for periodic flows, SIAM J. Appl. Math. 54 (1992), 333-408 | MR 1265233 | Zbl 0796.76084

, ,[10] Comparison of turbulent flame speeds from complete averaging and the G-equation, Phys. Fluids 7 no. 8 (1995), 2052-2060 | MR 1346082 | Zbl 1039.80504

, , ,[11] Partial Differential Equations, Graduate Studies in Mathematics, AMS, Providence, RI (1998) | MR 1625845

,[12] Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, CBMS-NSF Regional Conference Series in Applied Mathematics vol. 11, SIAM, Philadelphia (1973) | MR 350216

,[13] Large scale front dynamics for turbulent reaction–diffusion equations with separated velocity scales, Nonlinearity 7 (1994), 1-30 | MR 1260130 | Zbl 0839.76093

, ,[14] Flame fronts in a turbulent combustion model with fractal velocity fields, Comm. Pure Appl. Math. 51 (1998), 1337-1348 | MR 1639220 | Zbl 0939.35097

, ,[15] Homogenization of the G-equation with incompressible random drift in two dimensions, Commun. Math. Sci. 9 no. 2 (2011), 561-582 | MR 2815685 | Zbl 1241.35021

, ,[16] Asymptotic spreading of KPP reactive fronts in incompressible space–time random flows, Ann. Inst. Henri Poincaré, Anal. Non Lineaire 26 no. 3 (May–June 2009), 815-839 | Numdam | MR 2526403

, ,[17] Bounds on front speeds for inviscid and viscous G-equations, Methods Appl. Anal. 16 no. 4 (2009), 507-520 | MR 2734499 | Zbl 1256.35090

, , ,[18] Boundary layers and KPP fronts in a cellular flow, Arch. Ration. Mech. Anal. 184 no. 1 (2007), 23-48 | MR 2289862 | Zbl 1109.76064

, ,[19] A. Oberman, Ph.D thesis, University of Chicago, 2001.

[20] Level Set Methods and Dynamic Implicit Surfaces, Applied Mathematical Sciences vol. 153, Springer, New York (2003) | MR 1939127 | Zbl 1026.76001

, ,[21] Turbulent Combustion, Cambridge University Press, Cambridge (2000) | MR 1792350 | Zbl 0955.76002

,[22] Some open issues in premixed turbulent combustion, , (ed.), Modeling in Combustion Science, Lecture Notes in Physics vol. 449, Springer-Verlag, Berlin (1995), 3-22

,[23] Cascade-renormalization theory of turbulent flame speed, Combust. Sci. Techol. 62 (1988), 77-96

,[24] Renormalization concept of turbulent flame speed, Lecture Notes in Physics vol. 351 (1989) | MR 1037592

,[25] Turbulent combustion, (ed.), The Mathematics of Combustion, SIAM, Philadelphia (1985), 97-131 | MR 806548

,[26] Front propagation in heterogeneous media, SIAM Rev. 42 no. 2 (June 2000), 161-230 | MR 1778352

,[27] An Introduction to Fronts in Random Media, Surveys and Tutorials in the Applied Mathematical Sciences vol. 5, Springer (2009) | MR 2527020 | Zbl 1188.35003

,[28] Periodic homogenization of inviscid G-equation for incompressible flows, Commun. Math. Sci. 8 no. 4 (2010), 1067-1078 | MR 2744920 | Zbl 05843226

, ,[29] Propagation velocity of premixed turbulent flames, Combust. Sci. Techol. 60 (1988), 191-241

,