6 problems

Let $d$ be the spatial dimension, let $v(x)=|x|^{-\alpha}$ with $0<\alpha\leq 1$, and consider … with $0<\beta\leq 1/d$. Let $I^1$ denote the trace-class space used for the density…

Consider the time-dependent density-matrix equation with self-interaction satisfying condition (SI2), and let $d$ denote the spatial dimension and $\beta$ the exponent in that cond…

Facca–Cardaliaguet–Puel convergence conjecture. The long-time asymptotics of the solution $\mu(t,\cdot)$ is precisely the optimal transport density $\mu^*$, regardless of the chose…

Consider the autonomous Galerkin systems associated with the positive cubic beam problem, with Fourier modes $varphi_j$ and the notion of full instability defined by the two condit…

The cubic beam equation exhibits energy-exchange behavior beyond the parity-based closure observed in the half-linear case. Cubic energy-exchange conjecture. The general rule for t…

The paper considers the least Rayleigh quotient $lambdap$ associated with the homogeneous functional and the convergence results established under the assumption that $lambdap$ i…