2 problems

Let $u$ solve the incompressible Navier–Stokes equations on $[0,1]\times\mathbb{R}^3$, … For any $\alpha\in[0,1/2)$, consider initial data $u_0\in H^\alpha\cap L^{3,\infty}$ and so…

Let $u^0 ot\equiv 0$ belong to $H^s_{as\&df}(\mathbb{R}^d)$, where $d\geq 4$ and $s>1+\frac{d}{2}$, and let $\omega^0$ be its associated vorticity. Assume that $\omega^0$ is odd in…