4 problems

Let a viscosity solution be a 2D Euler solution obtained as a zero-viscosity limit of 2D Navier–Stokes solutions, and call it dissipative when $Z_h(\omega)\geq 0$ for convex $h$. U…

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

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…

Let $d\geq 2$ and $p>2$ be fixed. For a divergence free velocity field $b\in L^{\infty}([0,1],W^{1,p}(\mathbb{T}^d,\mathbb{R}^d))$ and an initial datum…