2 problems

Let $M\subset\mathbb{R}^2$ be any simply connected domain such that the constant-vorticity Euler solution $u_*$ on $M$ has a single eddy, meaning that its streamfunction has a sing…

Let $u$ solve the two-dimensional Navier–Stokes equations with viscosity $u$, and let $\overline{u}$ denote the corresponding Euler solution. Suppose the vanishing viscosity limit…