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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 convergeto solutions of the KSE on the time interval of existence and uniqueness of theKSE at an algebraic rate. In addition, we provide simulations of the calmedKSE, illuminating its dynamics. These simulations also indicate that ouranalytical predictions of the convergence rates are sharp. We also discussanalogies with the 3D Navier-Stokes equations of fluid dynamics.

Algebraic calming for the 2D Kuramoto-Sivashinsky equations