(untitled) (Journal of Mathematical Study, 2025)
A forced solution v of the axially symmetric Navier-Stokes equation in a finite cylinder D with suitable boundary condition is constructed. The forcing term, whose order of scaling is slightly worse than the critical order −2, is in the mildly super critical space L^q_tL^1_x for all q>1. The velocity, which is smooth until its final blow up moment, is in the energy space throughout.