The compressible boundary layer equations describe the behavior of the thin layer of fluid adjacent to a solid surface in a compressible fluid flow. One of the key parameters characterizing compressible boundary layers is the local Mach number ($M$), defined as the ratio of the local flow velocity to the local speed of sound, such as density variations, pressure gradients, and changes in the speed of sound. These equations can be quite complex and often require numerical methods, such as computational fluid dynamics (CFD), for solution.

Where:

• $U$ is the local flow velocity (m/s),
• $c$ is the local speed of sound (m/s).