MathDB5 problems
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Conjecture on covariance-independent continuous dependence for stochastic Navier–Stokes equations
Covariance-independent regularity conjecture. With suitable improvements of some of the arguments given in the paper, one can prove continuous dependence in a suitable space of reg…
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Batchelor Scale Conjecture for dissipation in stochastic and hyperviscous Navier–Stokes flows
Let 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…
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Acceleration of singularity formation under Lévy forcing
Consider the fractional stochastic Navier–Stokes system studied in the paper, but replace its Gaussian white-noise forcing by discontinuous forcing generated by a Lévy process with…
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Extension of statistical estimates to general multiplicative noise
Extension conjecture. The results presented in the manuscript may also be extended to this setting, potentially under a smallness condition on the diffusion coefficient.
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The full-horseshoe conjecture for GSNS
Full-horseshoe conjecture. GSNS has full-horseshoes on any two disjoint closed balls.