Source norms of the first velocity-improvement round #
The first round of prop:bootstrap starts from a velocity in
M^{3,25/3} and a gradient in M^{2,25/8} on a parabolic ball, and the
pressure gradient of eq:local-equation is already known in M^{6/5,25/11}
there. The exponents of the heat slot are the paper's
1/κ₂ = 1/τ + 1/τ₃ = 3/25 + 8/25 = 11/25, so the localized source
localizedGradientSourceG lies in M^{6/5,25/11}.
The derivative slot localizedGradientSourceH is a bounded multiple of the
velocity itself, so its integrability exponent stays at 3: it is estimated
in M^{3,25/6} directly, by lowering only the Morrey exponent from 25/3.
The two source slots of eq:local-equation at the first-round exponents.
The heat slot lands in M^{6/5,25/11} and the derivative slot in
M^{3,25/6}, both on the arbitrary parabolic ball carrying the cutoff.