11 problems

Lions's conjecture. The compressible Navier–Stokes system may exhibit propagation of oscillations; Lions provided an example for a variant of the system that includes a forcing ter…

Asymptotic-limit conjecture. The limit satisfies

Consider the one-dimensional hypo-viscous compressible Navier–Stokes equations with viscosity exponent $\beta=\frac{1}{2}$. Here $B_{2,1}^{\frac{1}{2}}$ denotes the critical Besov…

Nash's conjecture. One should be able to prove a conditional existence, smoothness, uniqueness, and continuation theorem for flow equations, conditional on the non-appearance of gr…

Planar Riemann-problem conjecture. The large-time asymptotic behavior of the solutions to the three-dimensional compressible Navier–Stokes system with different end states and with…

Consider the compressible Navier–Stokes equations referred to as, and backward self-similar solutions with radial symmetry. Nonexistence conjecture. There are no backward self-simi…

Let $\mu_A$ denote the invariant measure constructed for the one-dimensional stochastic compressible Navier–Stokes equations with noise amplitude parameter $A$. The unforced system…

Optimal-index conjecture. The optimal index might be

Inviscid diffusion-wave conjecture. Since the diffusion wave is independent of the viscosity, the result of Huang et al. should remain valid when

The algorithm uses $N_{Pic}$ Picard iterations, typically with $N_{Pic}\in\{p_{\gamma}+1,p_{\gamma}+2\}$, where $p_{\gamma}$ is the polynomial degree in time; for ordinary differen…

Let $N”$ denote the number of scalar Neumann conditions imposed in the viscous problem and let $N^2_-$ denote the number of outgoing characteristic modes associated with the releva…