On third order density contrast expansion of the evolution equation for wrinkled unsteady premixed flames

► We wish to derive pertinent evolution equations for premixed wrinkled flames. ► The Michelson-Sivashinsky perturbative approach is extended to 3rd order in gamma. ► Obtained flame shape and speed quantitatively compare to 1st order equation S1. ► An S1-type model equation is proposed, with only one gamma-dependent coefficient.