14 problems

Gevrey regularity conjecture. Any finite-regularity solution of the spatially inhomogeneous Boltzmann equation belongs to the Gevrey class

Let $s$ denote the Gevrey index governing the regularity of the solutions in the Vlasov–Poisson–Landau equation. Sharp Gevrey-index conjecture. The result may hold down to the shar…

Chueshov's conjecture. The semigroup $\{e^{\mathcal{A}t}\}_{\mathcal{L}(\mathcal{H})}$ is analytic in an appropriate sector of the complex plane.

The three-dimensional Couette-flow problem is studied in a setting where regularity is measured in Gevrey classes. Gevrey-3 lower-bound conjecture. The required regularity cannot b…

Let $U_{\rm sh}$ be a shear flow, and consider nonlinear hyperbolic equations admitting shear-flow solutions and the setting of Theorem. Gevrey-3 stability conjecture. Theorem hint…

Gevrey geodesic conjecture. Generic, in some sense, analytic metrics are linked by a $\frac{4}{3}$-Gevrey geodesic.

Optimal stability-space conjecture. The optimal space for stability is given by this Fourier weight.

Let $M$ be a quantizable compact Gevrey Kähler manifold, and let $s>1$ be its Gevrey order. In the Gevrey version of the Bergman-kernel expansion, the asymptotic summation is perfo…

Let $V$ be a neighborhood with a Kähler potential $\phi$ in Gevrey class $G^a(V)$, where $a>1$, and let $b_m(x,\bar{x})$ be the Bergman kernel coefficients. Write $v=(x,z)$, let…

Let $\mathbb H_n$ be the Heisenberg group, let $\gamma^{s}_{\mathbf{X},L^2}(\mathbb H_n)$ and $\gamma^{(s)}_{\mathbf{X},L^2}(\mathbb H_n)$ be the corresponding sub-Laplacian Gevrey…

Let $s eq 1$? No: the source considers $1leq s<infty$. Let $gamma^{s}{mathbf{X},L^2}(SU(2))$ and $gamma^{(s)}{mathbf{X},L^2}(SU(2))$ be the corresponding sub-Laplacian Gevrey space…

In the Sitnikov problem, let $e\in(0,1)$ denote the eccentricity, and in the restricted planar three-body problem (RPTBP), let $\mu\in(0,1/2]$ denote the mass parameter. An invaria…

Let $0<\nu<1$ be the order of the singular cross section kernel, and let $f$ be a weak solution of the non-cutoff homogeneous Boltzmann equation in $\mathbb{R}^d$ with initial datu…

Let $u(x,t)$ be the solution considered in Theorem 1.3, with $t>0$. Meromorphic–Gevrey representation conjecture. The function $u(x,t)$ could be represented, for any $t>0$, as a me…