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 $u^0 otequiv 0$ belong to H^s{as&df}(\mathbb{R}^d), where $dgeq 4$ and $s1+\frac{d}{2}$, and let $\omega^0$ be its associated vorticity. Assume that $\omega^0$ is odd in $z$ and…