Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number (Q1749352)

The authors present a first theoretical result to prove that the turbulent flame speed is decreasing with respect to the curvature diffusivity (Markstein number) for shear flows in the well-known G-equation model. In fact, they present the question Q1: How does the ``averaged'' flame propagation speed depend on the curvature term? Then they formulate it as Q2: How does \(\overline{H}_d(p)\) depend on the Markstein number \(d\)? In particular, is it decreasing with respect to \(d\)? In the main theorem, they show that \(\overline{H}_d\) is strictly decreasing with respect to the Markstein number. For the proof, they study the nonlinear structure of the involved equation.