4 problems

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…

Consider the one-dimensional thick-spray system given by equations $(,,,)$, with friction parameter $\beta\in\mathbb{R}$; the second case is the regime in which the acoustic waves…

Let $\varphi$ be a solution of the integral inequality … where $\overline{K}^{(\alpha)}$ is the kernel defined earlier in the paper, and let $\Phi$ denote the baby-model solution a…

Let $f:\mathbb R^d\to\mathbb C$ satisfy the hypotheses of the interpolation lemma, and let $\varepsilon\in(0,1/4)$. Denote by the optimal constant in the right-hand side of the int…