Radon measure‐valued solutions of compressible Euler equations and concentration boundary layers in unsteady inviscid flows passing solid obstacles

Abstract For time‐dependent compressible Euler flows passing around a fixed solid body in three‐dimensional space, there may exist an infinitesimally thin layer of concentrated mass, momentum and energy, wherein all particles impacting the body move along the body's windward boundary surface. By proposing a concept of Radon measure‐valued solutions for initial‐boundary‐value problems of the unsteady compressible Euler equations, which captures both the large‐scale three‐dimensional distributions of the surrounding flows and the small‐scale motions of particles on the two‐dimensional boundary surfaces, we derive the governing partial differential equations for the concentration boundary layer—an unsteady (pressureless) compressible Euler system defined on the boundary surface with appropriate source terms. This down‐scaling approach can be further generalized to incorporate skin‐frictions and phase‐transitions within the concentration boundary layer. It constitutes a novel methodology for addressing the complex fluid–solid–heat coupling problems encountered in fluid dynamics. Illustrative examples are presented to demonstrate the applicability of the proposed method to several specific problems, including the derivation for the most general case the Newtonian–Busemann pressure law of hypersonic aerodynamics.