On the nonlinear theory of hydrodynamic instability in flames

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Abstract
In the context of the weak thermal-expansion approximation, we derive an equation describing flame front dynamics under conditions of Darrieus-Landau instability. We show that the second-order theory leads to an evolution equation that differs from that of the first-order theory only in its coefficients. We also discuss a hydrodynamic flame model based on the equations for purely irrotational flow of the gas
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