Asymptotic solution of a problem in the ignition of a gas-fuel mixture by thermal flux of constant intensity (Q1803117)

The author solves the Cauchy problem for Navier-Stokes equations with boundary conditions. For the effectively unviscous gas mixture \((\text{Re}\gg 1)\) it is necessary to solve only Euler equations with no- slip conditions on the boundary. Applying the energy and continuity equations, the author obtains the temperature equation and the velocity distribution in boundary layer. Different asymptotic solutions are constructed in four possible zones of the fluid: 1) in boundary layer near the walls; 2) in the uniform flow of burnt gas; 3) in the stationary zone of flame; 4) in the uniform flow of unburnt mixture.