10 problems

Let $u_0\in L^2$ be initial data, and consider sequences of Leray–Hopf weak solutions of the Navier–Stokes equations whose inviscid limits are denoted by $u$. The critical Besov cl…

Prevalent singularity spectrum conjecture. For every $f\in\widetilde{b}^{\mu,\Psi}_{p,q}([0,1]^d)$,

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…

Lee–Rogers–Seeger local space-time conjecture. The estimate

Frisch–Parisi conjecture. In that Baire functional space, any typical element $f$ obeys some multifractal formalism and satisfies

With $\mathfrak{W}$, $\Omega$, $d$, $\ell$, $k$, and $S^{d-1}$ as above, for $\alpha\in(0,d)$, the Besov--Lorentz strengthening. The Riesz potential $\operatorname{I}_{\alpha}$ map…

Let $w_{\alpha}$ denote a periodic symmetric-$\alpha$-stable noise on $\mathbb{T}^d$, with $0<p<\alpha<2$. The endpoint regularity conjecture. … The paper obtains regularity result…

Let $w$ be a periodic noise on $\mathbb{T}^d$, let $\tau\bin\tyu0005\mathbb{R}$, and let $0<p,q\textless\textless=\infty$. The zero–one law. For every such noise and every such Bes…

Let $\theta$ be a one-component inner function, let $\mathcal K_\theta=H^2\ominus\theta H^2$, and let $\Gamma_{\phi}:\mathcal K_\theta\to\overline{z\mathcal K_\theta}$ be a truncat…

Let $D=d+d'$ and let $B^{s}_{p,q}(\mathbb{R}^D)$ be the Besov space under the hypotheses on $p,q,s$ of Theorem. For a $d$-dimensional subspace $\mathcal{H}$ of $\mathbb{R}^D$, writ…