The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equation

Excerpt

arXiv:2608.15337v1 Announce Type: cross Abstract: We disprove the expectation stated by Xin, Yu, and Ronney that the physical positive part strain $G$-equation should possess an effective burning velocity in cellular flows. For the standard cellular flow in dimension two $V_A(x_1,x_2)=A(-\sin x_1\cos x_2,\cos x_1\sin x_2)$, if $0<20/399$ and $\sqrt{1+4d^2}0$ universal. The same conclusions hold for arbitrary continuous periodic perturbations of planar initial data. Under the physical scaling $V_