2 problems

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Batchelor Scale Conjecture for dissipation in stochastic and hyperviscous Navier–Stokes flows
Let $u$ be a velocity field given by either a two-dimensional stochastic Navier–Stokes equation or a three-dimensional hyperviscous Navier–Stokes equation. For the passive scalar a…
Conjectureopenbatchelor-scale passive-scalar-mixing stochastic-navier-stokesarXiv posted 2 days ago
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The larger-domain stirring conjecture for passive scalar mixing
Larger-domain stirring conjecture. The scalar might be mixed faster on the larger domain $[0,N \times L]^3$ than on the elementary cell $[0,L]^3$ .
Conjectureopenfluid-dynamics mixing passive-scalar-mixingarXiv posted 2 days ago

Batchelor Scale Conjecture for dissipation in stochastic and hyperviscous Navier–Stokes flows