4 problems

Strictness characterization.

Steady-state convergence conjecture. The solution $\mathbf{u}$ converges towards a steady state.

Fix $p\in[1,+\infty)$. Let $b\in C^{\infty}([0,T]\times\mathbb{T}^d)$ be divergence free and let $u_0\in W^{1,2}(\mathbb{T}^d)$. If $u^\nu$ is a solution of the advection diffusion…

Cantrell-Cosner-Lou concentration conjecture. $u$ concentrates precisely on the set of positive local maximum points of $m(x)$ as $\alpha\rightarrow\infty$.