2 problems

Let $\Omega$ be a multiply connected fluid domain with boundary decomposed into entering, exiting, and impermeable parts $\Gamma_{\mathrm{in}}$, $\Gamma_{\mathrm{out}}$, and…

Let $\omega_0\in H^1(\mathbb{T}^2)\cap L^\infty(\mathbb{T}^2)$ be mean-zero, and let the corresponding solution of the two-dimensional incompressible Euler equations be a Yudovich…