MathDB4 problems
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The role of dispersive focusing in promoting nonlinear wave interaction and transition to turbulence
Dispersive-focusing conjecture. Dispersive focusing in the early evolution of a wave packet may play an important role in promoting nonlinear wave interaction and the consequent tr…
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Trefethen et al.'s transition-threshold conjecture for the Navier–Stokes equations
Trefethen et al.'s conjecture. The amplitude threshold of transition for the Navier–Stokes equations is
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Trefethen et al.'s transition-threshold conjecture for eigenvalue-stable shear flows
Trefethen et al.'s conjecture. Transition to turbulence of eigenvalue-stable shear flows should be driven by an essentially linear destabilizing mechanism, with amplitude threshold
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The stable-manifold mechanism for transition from linear shear to turbulence
The linear shear is linearly stable, so its stable manifolds cannot be connected directly to the linear shear. The relevant stable manifolds are those of the recently discovered th…