2 problems

Let $\boldsymbol{u}^ u,\boldsymbol{ abla}\boldsymbol{\times}\boldsymbol{u}^ u=\boldsymbol{ abla}\times\boldsymbol{u}^ u$ be a sequence of 2D Navier–Stokes solutions satisfying the…

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…