We propose an approximate model for the 2D Kuramoto-Sivashinsky equations (KSE) of flame fronts and crystal growth. We prove that this new ``calmed'' version of the KSE is globally well-posed, and moreover, its solutions converge to solutions of the KSE on the time interval of existence and uniqueness of the KSE at an algebraic rate. In addition, we provide simulations of the calmed KSE, illuminating its dynamics. These simulations also indicate that our analytical predictions of the convergence rates are sharp. We also discuss analogies with the 3D Navier-Stokes equations of fluid dynamics.

翻译：本文针对火焰锋面和晶体生长的二维Kuramoto-Sivashinsky方程（KSE）提出了一种近似模型。我们证明了这个新的“镇定”版KSE方程整体适定，并且其解在KSE存在唯一解的时间区间上以代数速率收敛至KSE的解。此外，我们通过数值模拟展示了镇定KSE的动力学特性，这些模拟同时表明我们对收敛速率的理论预测是最优的。文中还讨论了与流体动力学中三维Navier-Stokes方程的类比关系。