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 $2<p<\infty$. Consider the two-dimensional Euler equation with initial velocity $v^\circ\in L^2$ and initial vorticity $\omega^\circ\in L^1\cap L^p$. A weak solution has veloci…