3 problems

Supercritical nonuniqueness and non-Leray-Hopf conjecture. Then there exist two weak solutions $u,v\in X^{p,q}([0,T];\mathbb{T}^d)$ of the Navier–Stokes equations with

Higher-dimensional convergence conjecture. The sequence $cv_n$ is bounded in $W_0^{1,2}(\Omega)\cap L^\infty(\Omega)$ and therefore converges, up to subsequences, to a bounded nonn…

Let $T>0$) and $R>0$. Let $\mathcal{X}_{01}=(U_{01},U_{11})$ and $\mathcal{X}_{02}=(U_{02},U_{12})$ belong to $\mathcal{H}_0$, with $\mathcal{X}_{01}$ and $\mathcal{X}_{02}$ having…