7 problems

Uniqueness conjecture. The sequence $bm{nu}^{\infty}={nu_{k}}_{k}$ is the unique solution in $L^{\infty}([0,\infty),\mathcal{X})$ to the annihilated Boltzmann hierarchy in the sense o…

Regularity propagation conjecture. The local solution $f(t)$ carries the $\frac{1}{2}+$ regularity of the initial data up to time $T_0$; in particular, for every $T\in(0,T_0)$,

Let $B$ be a collision cross-section satisfying condition with homogeneity $\gamma<\gamma_{\mathrm{crit}}=-\frac32$, and let $g(t,w)$ be a weak solution of the cylindrical-dilatati…

Let $B$ be a collision cross-section satisfying condition, and let $\gamma$ denote its homogeneity. Let $Q(t)$ and $L_0$ be the matrix-valued quantities appearing in the homoenerge…

Let $B$ be a Boltzmann collision kernel with parameters $\gamma\in(-d,\infty)$ and $\alpha\in[0,2)$. A spectral gap means that the associated linearized Boltzmann collision operato…

Let $L(t)$ denote the limiting family of linear operators arising in the scaling limit where the quantum wavelength and scattering radius satisfy $h=r\to0$, with observables evolve…

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…