G-equation is a popular level set model in turbulent combustion, and becomes an advective mean   curvature type evolution equation when the curvature effect is considered:

$$G_t + \left(1-d\, \Div{\frac{DG}{|DG|}}\right)_+|DG|+V(x)\cdot DG=0.$$

In this talk, I will show the existence of effective burning velocity under the above curvature G-equation model when $V$ is a two dimensional cellular flow. Our proof combines PDE methods with a dynamical analysis of the Kohn-Serfaty deterministic game characterization of the curvature G-equation based on the special structure of the cellular flow. This is a joint with Hongwei Gao, Ziang Long and Jack Xin.

会议密码:225926