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Abstract. We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable.

Eddington factors are a common ingredient in many techniques for solving radiation hydrodynamics problems. Usually they are introduced in a phenomenological or ad hoc manner. In this paper a fundamental approach is devised for justifying Eddington factors on the basis of mathematical requirements arising from nonequilibrium thermodynamics.

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