3 problems

Let $u$ be a weak solution of the Euler equations whose spatial regularity is below $1/3$ of a derivative, or whose time integrability is below $q=\infty$, and let $e(t)$ denote it…

Let $(u,b)$ be a weak solution of the ideal MHD system, and define the total energy and cross helicity by … … Here $C_{x,t}^\alpha$ denotes joint Hölder regularity and…

Let $d\in\{2,3\}$. Let $u\in C^0([0,1];C^\alpha(\mathbb T^d))\cap C^\alpha([0,1];C^0(\mathbb T^d))$ be a weak solution of the incompressible Euler equations, for some Hölder expone…