6 problems

Silvestre and Vicol's conjecture. Such solutions should be bounded in $C^{1/2}$ for every $t>0$.

Let $\theta(y,t)$ be a smooth, even solution of the Córd​​oba–Córd​​oba–Fontelos equation … with initial condition having a single nondegenerate maximum and decaying sufficiently q…

Let $\theta_0$ satisfy the hypotheses of the Hölder $1/2$ a priori estimate conjecture, and let $\theta$ be a vanishing-viscosity limit of solutions of … Here…

Let $\theta_0$ be initial data satisfying the hypotheses of the Hölder $1/2$ a priori estimate conjecture, and consider the supercritically dissipative Hilbert model … with…

Let $\theta$ be a bounded solution on $[0,T]$ of … where $H$ is the Hilbert transform. The $C^{1/2}$ Hölder seminorm measures the quotient $|\theta(t,x)-\theta(t,y)|/|x-y|^{1/2}$.…

Let $\theta$ solve the one-dimensional nonlocal transport equation … where $H$ is the Hilbert transform, and let $C^{1/2}$ denote the Hölder class with exponent $1/2$. A Hölder reg…