Blow-up of the hyperbolic Burgers equation

The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification of the Burgers equation, that has been introduced to clarify the interplay of hyperbolicity and nonlinear hydrodynamic evolution. Previous studies suggested the finite time blow-up of this equation, and here we present a rigorous proof of this fact

Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non BV perturbations

We develop a theory based on relative entropy to show the uniqueness and L^2 stability (up to a translation) of extremal entropic Rankine-Hugoniot discontinuities for systems of conservation laws (typically 1-shocks, n-shocks, 1-contact discontinuities and n-contact discontinuities of large amplitude) among bounded entropic weak solutions having an additional trace property. The existence of a convex entropy is needed. No BV estimate is needed on the weak solutions considered. The theory holds without smallness condition. The assumptions are quite general. For instance, strict hyperbolicity is not needed globally. For fluid mechanics, the theory handles solutions with vacuum.Comment: 29 page

Global generalized solutions for Maxwell-alpha and Euler-alpha equations

We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.Comment: 27 pages, to appear in Nonlinearit

Аліментні обов'язки інших членів сім'ї та родичів

Виявлено проблеми у врегулюванні аліментних обов’язків інших членів сім’ї та родичів, вироблено рекомендації щодо їх вирішення. Проаналізовано специфіку правового регулювання аліментних зобов’язань зазначених суб’єктів, сімейне законодавство та міжнародний досвід. Ключові слова: аліментні обов’язки, правове регулювання, сімейне законодавство.Выявлены проблемы в урегулировании алиментных обязанностей других членов семьи и родственников, выработаны рекомендации по их решению. Проанализирована специфика правового регулирования алиментных обязательств указанных субъектов, семейное законодательство и международный опыт. Ключевые слова: алиментные обязанности, правовое регулирование, семейное законодавствоThis article is dedicated to identifying problems in the regulation of the alimentary obligations of other family members and relatives, and to making recommendations and proposing solutions. Studing the specificity of the legal regulation of alimentary obligations of these entities, analysing the current family law and international experience are very important. Key words: alimentary obligations, legal regulation, family law

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Uniform regularity for the Navier-Stokes equation with Navier boundary condition

We prove that there exists an interval of time which is uniform in the vanishing viscosity limit and for which the Navier-Stokes equation with Navier boundary condition has a strong solution. This solution is uniformly bounded in a conormal Sobolev space and has only one normal derivative bounded in $L^\infty$. This allows to get the vanishing viscosity limit to the incompressible Euler system from a strong compactness argument

Optimizing Research to Speed Up Availability of Pediatric Antiretroviral Drugs and Formulations

Globally 1.8 million children are living with human immunodeficiency virus (HIV), yet only 51% of those eligible actually start treatment. Research and development (R&D) for pediatric antiretrovirals (ARVs) is a lengthy process and lags considerably behind drug development in adults. Providing safe, effective, and well-tolerated drugs for children remains critical to ensuring scale-up globally. We review current approaches to R&D for pediatric ARVs and suggest innovations to enable simplified, faster, and more comprehensive strategies to develop optimal formulations. Several approaches could be adopted, including focusing on a limited number of prioritized formulations and strengthening existing partnerships to ensure that pediatric investigation plans are developed early in the drug development process. Simplified and more efficient mechanisms to undertake R&D need to be put in place, and financing mechanisms must be made more sustainable. Lessons learned from HIV should be shared to support progress in developing pediatric formulations for other diseases, including tuberculosis and viral hepatitis

On Landau damping

Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation; new functional inequalities; a control of nonlinear echoes; sharp scattering estimates; and a Newton approximation scheme. Our results hold for any potential no more singular than Coulomb or Newton interaction; the limit cases are included with specific technical effort. As a side result, the stability of homogeneous equilibria of the nonlinear Vlasov equation is established under sharp assumptions. We point out the strong analogy with the KAM theory, and discuss physical implications.Comment: News: (1) the main result now covers Coulomb and Newton potentials, and (2) some classes of Gevrey data; (3) as a corollary this implies new results of stability of homogeneous nonmonotone equilibria for the gravitational Vlasov-Poisson equatio

Superconducting phases of f-electron compounds

Intermetallic compounds containing f-electron elements display a wealth of superconducting phases, that are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferro- and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconductivity near valence transitions, or in the vicinity of magneto-polar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of f-electron compounds is reviewed.Comment: Rev. Mod. Phys. in print; 75 pages, 23 figures; comments welcom

Effect of Deutetrabenazine on Chorea Among Patients With Huntington Disease A Randomized Clinical Trial

Importance Deutetrabenazine is a novel molecule containing deuterium, which attenuates CYP2D6 metabolism and increases active metabolite half-lives and may therefore lead to stable systemic exposure while preserving key pharmacological activity. Objective To evaluate efficacy and safety of deutetrabenazine treatment to control chorea associated with Huntington disease. Design, Setting, and Participants Ninety ambulatory adults diagnosed with manifest Huntington disease and a baseline total maximal chorea score of 8 or higher (range, 0-28; lower score indicates less chorea) were enrolled from August 2013 to August 2014 and randomized to receive deutetrabenazine (n = 45) or placebo (n = 45) in a double-blind fashion at 34 Huntington Study Group sites. Interventions Deutetrabenazine or placebo was titrated to optimal dose level over 8 weeks and maintained for 4 weeks, followed by a 1-week washout. Main Outcomes and Measures Primary end point was the total maximal chorea score change from baseline (the average of values from the screening and day-0 visits) to maintenance therapy (the average of values from the week 9 and 12 visits) obtained by in-person visits. This study was designed to detect a 2.7-unit treatment difference in scores. The secondary end points, assessed hierarchically, were the proportion of patients who achieved treatment success on the Patient Global Impression of Change (PGIC) and on the Clinical Global Impression of Change (CGIC), the change in 36-Item Short Form– physical functioning subscale score (SF-36), and the change in the Berg Balance Test. Results Ninety patients with Huntington disease (mean age, 53.7 years; 40 women [44.4%]) were enrolled. In the deutetrabenazine group, the mean total maximal chorea scores improved from 12.1 (95% CI, 11.2-12.9) to 7.7 (95% CI, 6.5-8.9), whereas in the placebo group, scores improved from 13.2 (95% CI, 12.2-14.3) to 11.3 (95% CI, 10.0-12.5); the mean between-group difference was –2.5 units (95% CI, –3.7 to –1.3) (P < .001). Treatment success, as measured by the PGIC, occurred in 23 patients (51%) in the deutetrabenazine group vs 9 (20%) in the placebo group (P = .002). As measured by the CGIC, treatment success occurred in 19 patients (42%) in the deutetrabenazine group vs 6 (13%) in the placebo group (P = .002). In the deutetrabenazine group, the mean SF-36 physical functioning subscale scores decreased from 47.5 (95% CI, 44.3-50.8) to 47.4 (44.3-50.5), whereas in the placebo group, scores decreased from 43.2 (95% CI, 40.2-46.3) to 39.9 (95% CI, 36.2-43.6), for a treatment benefit of 4.3 (95% CI, 0.4 to 8.3) (P = .03). There was no difference between groups (mean difference of 1.0 unit; 95% CI, –0.3 to 2.3; P = .14), for improvement in the Berg Balance Test, which improved by 2.2 units (95% CI, 1.3-3.1) in the deutetrabenazine group and by 1.3 units (95% CI, 0.4-2.2) in the placebo group. Adverse event rates were similar for deutetrabenazine and placebo, including depression, anxiety, and akathisia. Conclusions and Relevance Among patients with chorea associated with Huntington disease, the use of deutetrabenazine compared with placebo resulted in improved motor signs at 12 weeks. Further research is needed to assess the clinical importance of the effect size and to determine longer-term efficacy and safety