5 problems

Let $L$ be a high-order space discretization of a convective operator, such as an ENO discretization. The fifth-order WENO space discretization is not stable under Forward Euler ti…

Steady-state optimal heat transport conjecture. Steady solutions maximize heat transport among all solutions of the Boussinesq equations.

Conjecture on the optimal aspect ratio. For large $\text{\textit{Pe}}$,

Conjecture on the transport exponent. For large $\text{\textit{Pe}}$, the exponent $0.58$ is actually $10/17=0.5882\dots$, so that

The chaotic-regime Nusselt-number conjecture.