“…Using the sound framework of Recursive Analysis, we assert the computability of a local strong solution of (1) in the space L σ 2,0 (Ω) (see Section 2 for definition) from a given initial condition a ∈ L σ 2,0 (Ω); moreover, the computation is uniform in the initial data. We follow a common strategy used in the classical existence proofs [3,4,5,18,21]: i) Eliminate the pressure P by applying, to both sides of Equation (1), the Helmholtz projection P : L 2 (Ω) 2 → L σ 2,0 (Ω), thus arriving at the nonlinear evolution equation…”