The Vlasov--Poisson--Landau system in the weakly collisional regime

Consider the Vlasov--Poisson--Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu Q(F,F)(t,x,v),\\ E(t,x) = \nabla \Delta^{-1} (\int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v - \frac{1}{(2\pi)^3}\int_{\mathbb T^3} \int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v \, \mathrm{d} x), \end{aligned}$$ with $\nu\ll 1$. We prove that for $\epsilon>0$ sufficiently small (but independent of $\nu$), initial data which are $O(\epsilon \nu^{1/3})$-Sobolev space perturbations from the global Maxwellians lead to global-in-time solutions which converge to the global Maxwellians as $t\to \infty$. The solutions exhibit uniform-in-$\nu$ Landau damping and enhanced dissipation. Our main result is analogous to an earlier result of Bedrossian for the Vlasov--Poisson--Fokker--Planck equation with the same threshold. However, unlike in the Fokker--Planck case, the linear operator cannot be inverted explicitly due to the complexity of the Landau collision operator. For this reason, we develop an energy-based framework, which combines Guo's weighted energy method with the hypocoercive energy method and the commuting vector field method. The proof also relies on pointwise resolvent estimates for the linearized density equation.Comment: 78 Pages. Comments welcome

Evaluation of a quality improvement intervention for obstetric and neonatal care in selected public health facilities across six states of India

Background While increase in the number of women delivering in health facilities has been rapid, the quality of obstetric and neonatal care continues to be poor in India, contributing to high maternal and neonatal mortality. Methods The USAID ASSIST Project supported health workers in 125 public health facilities (delivering approximately 180,000 babies per year) across six states to use quality improvement (QI) approaches to provide better care to women and babies before, during and immediately after delivery. As part of this intervention, each month, health workers recorded data related to nine elements of routine care alongside data on perinatal mortality. We aggregated facility level data and conducted segmented regression to analyse the effect of the intervention over time. Results Care improved to 90–99% significantly (p < 0.001) for eight of the nine process elements. A significant (p < 0.001) positive change of 30–70% points was observed during post intervention for all the indicators and 3–17% points month-to-month progress shown from the segmented results. Perinatal mortality declined from 26.7 to 22.9 deaths/1000 live births (p < 0.01) over time, however, it is not clear that the intervention had any significant effect on it. Conclusion These results demonstrate the effectiveness of QI approaches in improving provision of routine care, yet these approaches are underused in the Indian health system. We discuss the implications of this for policy makers.by Enisha Sarin, Subir K. Kole, Rachana Patel, Ankur Sooden, Sanchit Kharwal, Rashmi Singh, Mirwais Rahimzai and Nige Livesle