Monotone energy stability of magnetohydrodynamics Couette and Hartmann flows

We study the monotone nonlinear energy stability of \textit{magnetohydrodynamics plane shear flows, Couette and Hartmann flows}. We prove that the least stabilizing perturbations, in the energy norm, are the two-dimensional spanwise perturbations and give some criti\-cal Reynolds numbers Re$_E$ for some selected Prandtl and Hartmann numbers. This result solves a conjecture given in a recent paper by Falsaperla et al. \cite{FMP.2022} and implies a Squire theorem for nonlinear energy: the less stabilizing perturbations in the \textit{energy norm} are the two-dimensional spanwise perturbations. Moreover, for Reynolds numbers less than Re$_E$ there can be no transient energy growth.Comment: 13 pages, 2 figure

Gaia Early Data Release 3: Structure and properties of the Magellanic Clouds

We compare the Gaia DR2 and Gaia EDR3 performances in the study of the Magellanic Clouds and show the clear improvements in precision and accuracy in the new release. We also show that the systematics still present in the data make the determination of the 3D geometry of the LMC a difficult endeavour; this is at the very limit of the usefulness of the Gaia EDR3 astrometry, but it may become feasible with the use of additional external data. We derive radial and tangential velocity maps and global profiles for the LMC for the several subsamples we defined. To our knowledge, this is the first time that the two planar components of the ordered and random motions are derived for multiple stellar evolutionary phases in a galactic disc outside the Milky Way, showing the differences between younger and older phases. We also analyse the spatial structure and motions in the central region, the bar, and the disc, providing new insights into features and kinematics. Finally, we show that the Gaia EDR3 data allows clearly resolving the Magellanic Bridge, and we trace the density and velocity flow of the stars from the SMC towards the LMC not only globally, but also separately for young and evolved populations. This allows us to confirm an evolved population in the Bridge that is slightly shift from the younger population. Additionally, we were able to study the outskirts of both Magellanic Clouds, in which we detected some well-known features and indications of new ones

The Gaia mission

Gaia is a cornerstone mission in the science programme of the EuropeanSpace Agency (ESA). The spacecraft construction was approved in 2006, following a study in which the original interferometric concept was changed to a direct-imaging approach. Both the spacecraft and the payload were built by European industry. The involvement of the scientific community focusses on data processing for which the international Gaia Data Processing and Analysis Consortium (DPAC) was selected in 2007. Gaia was launched on 19 December 2013 and arrived at its operating point, the second Lagrange point of the Sun-Earth-Moon system, a few weeks later. The commissioning of the spacecraft and payload was completed on 19 July 2014. The nominal five-year mission started with four weeks of special, ecliptic-pole scanning and subsequently transferred into full-sky scanning mode. We recall the scientific goals of Gaia and give a description of the as-built spacecraft that is currently (mid-2016) being operated to achieve these goals. We pay special attention to the payload module, the performance of which is closely related to the scientific performance of the mission. We provide a summary of the commissioning activities and findings, followed by a description of the routine operational mode. We summarise scientific performance estimates on the basis of in-orbit operations. Several intermediate Gaia data releases are planned and the data can be retrieved from the Gaia Archive, which is available through the Gaia home page. http://www.cosmos.esa.int/gai

On the Lyapunov stability of a plane parallel convective flow of a binary mixture

The nonlinear stability of plane parallel convective flows of a binary fluid mixture in the Oberbeck-Boussinesq scheme is studied in the stress-free boundary case. Nonlinear stability conditions independent of Reynolds number are proved

Some results in the nonlinear stability for rotating Bénard problem with rigid boundary condition

The scope of this article is to expose the stabilizing properties of rotation and solute gradient for the Bénard problem with (at least one-sided) rigid boundary conditions. We perform a linear investigation of the critical threshold for the rotating Bénard problem with a binary fluid, and we also make an investigation with a Lyapunov function for the particular problem of a rotating single fluid. In all the these cases an increase of the Taylor number has stabilizing effects

Preface

This issue is dedicated to the 6th International Biennial Conference on "Waves and Stability in Continuous Media"Acireale (Italy) May 27 – June

Does Symmetry of the Operator of a Dynamical System Help Stability?

In this article, we address the question of relating the stability properties of an operator with the stability properties of its associate symmetric operator. The linear-algebra results of Bendixson and Hirsch indicate that the symmetric part of a matrix is always less stable than the matrix itself. We show that in a variety of cases, including infinite dimen- sional cases associated to systems of PDEs, the same result is valid. We also discuss the applicability to non-autonomous systems, and we show that, in general, this result is not valid. We also review some of the literature that in these years has appeared on the subject