Local‐in‐time well‐posedness for the regular solution to the 2D full compressible Navier–Stokes equations with degenerate viscosities and heat conductivity

Abstract This paper considers the two‐dimensional Cauchy problem of the full compressible Navier–Stokes equations with far‐field vacuum in , where the viscosity and heat‐conductivity coefficients depend on the absolute temperature in the form of with . Due to the appearance of the vacuum, the momentum equations are both degenerate in the time evolution and spatial dissipation, which makes the study on the well‐posedness challenging. By establishing some new singular‐weighted (negative powers of the density ) estimates of the solution, we establish the local‐in‐time well‐posedness of the regular solution with far‐field vacuum in terms of , the velocity , and the entropy . Moreover, the uniform regularity of the entropy in is established, that is, for some constant .