Chapter 31: τ

We define the initial data and spatial domains for the τ-internal approach to Navier–Stokes regularity. The classical problem asks whether smooth initial data produce smooth solutions for all time; the τ-internal reformulation replaces “smooth” with “stabilised ω-germ” and replaces ℝ^3 with clopen cylinders in τ³. This chapter introduces τ-admissible fluid data (Definition III.D36) and clopen cylinder domains (Definition III.D37), and states the scope boundary (Remark III.R17) that governs all of Part V.