Ergodicity of the finite dimensional approximation of the 3D Navier-Stokes equations forced by a degenerate noise

We prove ergodicity of the finite dimensional approximations of the three dimensional Navier-Stokes equations, driven by a random force. The forcing noise acts only on a few modes and some algebraic conditions on the forced modes are found that imply the ergodicity. The convergence rate to the unique invariant measure is shown to be exponential

Markov selections for the 3D stochastic Navier-Stokes equations

We investigate the Markov property and the continuity with respect to the initial conditions (strong Feller property) for the solutions to the Navier-Stokes equations forced by an additive noise. First, we prove, by means of an abstract selection principle, that there are Markov solutions to the Navier-Stokes equations. Due to the lack of continuity of solutions in the space of finite energy, the Markov property holds almost everywhere in time. Then, depending on the regularity of the noise, we prove that any Markov solution has the strong Feller property for regular initial conditions. We give also a few consequences of these facts, together with a new sufficient condition for well-posedness.Comment: 59 pages; corrected several errors and typos, added reference

Regularity of transition semigroups associated to a 3D stochastic Navier-Stokes equation

A 3D stochastic Navier-Stokes equation with a suitable non degenerate additive noise is considered. The regularity in the initial conditions of every Markov transition kernel associated to the equation is studied by a simple direct approach. A by-product of the technique is the equivalence of all transition probabilities associated to every Markov transition kernel.Comment: 17 page

Impact of Continuing Education on Clinicians' Self- Reported Knowledge of Tobacco Dependence and Tobacco Control Interventions

Purpose: To assess a tobacco cessation continuing education (CE) program for Indiana dental and medical providers. Methods: A 26-item immediate post-CE survey and a 19-item 3-month follow-up survey assessed changes in participants’ self-reported knowledge of tobacco dependence and tobacco control interventions. De-identified data were analyzed using descriptive statistics, Spearman correlation coefficients, and Mantel- Haenszel chi-square tests. Results: Participants totaled 252 across 6 programs statewide. Immediate post-CE course survey response was 98.4% (N=248): dental assistants (2%), dental hygienists (83%), dentists (8.5%), and other healthcare professionals (6.45%). Participants reported less knowledge before than immediately after CE (p< .0001) and 3 months after (p<.0001). Reported knowledge at 3 months was less than after CE (p< .002). Participants reported on their intention to apply program communication strategies (99%), implement brief tobacco interventions (85%), and refer patients to local cessation resources (95%), Indiana Quitline (96%). Follow-up survey response rate was 54% (N=136). Participants reported active engagement in tobacco interventions (48%, 78), applying CE communication strategies (85%, 109), and implementing brief interventions (71%, 90). Participants reported referring few patients to local or state quitline counselors. Conclusion:Tobacco dependence CE may enhance health care practitioners’ knowledge and willingness to integrate tobacco interventions in their healthcare settings but it does not ensure a change in clinical tobacco control intervention