Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities

We show the existence of global weak solutions to the three-dimensional compressible primitive equations of atmospheric dynamics with degenerate viscosities. In analogy with the case of the compressible Navier-Stokes equations, the weak solutions satisfy the basic energy inequality, the Bresh-Desjardins entropy inequality and the Mellet-Vasseur estimate. These estimates play an important role in establishing the compactness of the vertical velocity of the approximating solutions, and therefore are essential to recover the vertical velocity in the weak solutions

Reproductive solution for grade-two fluid model in two dimensions

  We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.   We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.&nbsp

Reproductive solution for grade-two fluid model in two dimensions

  We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.   We treat the existence of reproductive solution (weak periodic solution) of a second-grade fluid system in two dimensions, by using the Galerkin approximation method and compactness arguments.&nbsp

Fabrication and characterization of Nb2O5-doped 3Y-TZP materials sintered by microwave technology

[EN] The purpose of this research is focused on the manufacture and characterization of a partially stabilized zirconia ceramic with 3 mol% of Yttria and doped with .5 and 1.5 mol% of Nb2O5 to analyze the influence of doping, with the purpose of improving the properties before hydrothermal degradation. In the first instance, the microwave sintering process was used for the consolidation of this material, then the physical and mechanical properties were characterized. Together, the results obtained by the conventional sintering process were compared. A low hydrothermal degradation study (LTD) is presented at low temperatures in which possible changes in the mechanical properties of the ceramic materials are analyzed and its influence on the phase transformation that zirconia may present is observed. The mechanical properties were evaluated through hardness, fracture toughness, and Young's modulus tests. Likewise, their density was analyzed, and microstructure was characterized by FESEM. It was found that the microwave-sintered samples at 1200 degrees C exhibited superior properties of toughness than even samples sintered by conventional methods at higher temperatures (1400 degrees C). The sample of 3Y-TZP with 1.5 mol% Nb2O5 sintered by microwave with <.2% of porosity achieved a maximum fracture toughness value around 40% higher than the dense monolithic 3Y-TZP material.Santiago Grisolia program, Grant/Award Number: GRISOLIAP/2018/168; Ministry of Science, Innovation and Universities (Spain), Grant/Award Numbers: RTI2018-099033-B-C32, RYC-2016-20915Guillén-Pineda, RM.; Salvador Moya, MD.; Gutiérrez-González, CF.; Catalá Civera, JM.; Borrell Tomás, MA. (2021). Fabrication and characterization of Nb2O5-doped 3Y-TZP materials sintered by microwave technology. International Journal of Applied Ceramic Technology. 18(6):2033-2044. https://doi.org/10.1111/ijac.138572033204418

Detailed studies of IPHAS sources -- III. The highly extinguished bipolar planetary nebula IPHASX J191104.8++060845

We present the first detailed study of the bipolar planetary nebula (PN) IPHASX J191104.8$+$060845 (PN G040.6$-$01.5) discovered as part of the Isaac Newton Telescope Photometric H$\alpha$ Survey of the Northern Galactic plane (IPHAS). We present Nordic Optical Telescope (NOT) narrow-band images to unveil its true morphology. This PN consists of a main cavity with two newly uncovered extended low-surface brightness lobes located towards the NW and SE directions. Using near-IR WISE images we unveiled the presence of a barrel like structure, which surrounds the main cavity, which would explain the dark lane towards the equatorial regions. We also use Gran Telescopio de Canarias (GTC) spectra to study the physical properties of this PN. We emphasise the potential of old PNe detected in IPHAS to study the final stages of the evolution of the circumstellar medium around solar-like stars.Comment: 9 pages, 8 Figures, 3 Tables; Accepted to MNRA

Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise

The Primitive Equations are a basic model in the study of large scale Oceanic and Atmospheric dynamics. These systems form the analytical core of the most advanced General Circulation Models. For this reason and due to their challenging nonlinear and anisotropic structure the Primitive Equations have recently received considerable attention from the mathematical community. In view of the complex multi-scale nature of the earth's climate system, many uncertainties appear that should be accounted for in the basic dynamical models of atmospheric and oceanic processes. In the climate community stochastic methods have come into extensive use in this connection. For this reason there has appeared a need to further develop the foundations of nonlinear stochastic partial differential equations in connection with the Primitive Equations and more generally. In this work we study a stochastic version of the Primitive Equations. We establish the global existence of strong, pathwise solutions for these equations in dimension 3 for the case of a nonlinear multiplicative noise. The proof makes use of anisotropic estimates, $L^{p}_{t}L^{q}_{x}$ estimates on the pressure and stopping time arguments.Comment: To appear in Nonlinearit