Global solutions to the three-dimensional full compressible magnetohydrodynamic flows

The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional full magnetohydrodynamic equations with large data is established

Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $\gamma>\frac32$ and constant viscosity coefficients

Isometric Immersions and Compensated Compactness

A fundamental problem in differential geometry is to characterize intrinsic metrics on a two-dimensional Riemannian manifold ${\mathcal M}^2$ which can be realized as isometric immersions into $\R^3$. This problem can be formulated as initial and/or boundary value problems for a system of nonlinear partial differential equations of mixed elliptic-hyperbolic type whose mathematical theory is largely incomplete. In this paper, we develop a general approach, which combines a fluid dynamic formulation of balance laws for the Gauss-Codazzi system with a compensated compactness framework, to deal with the initial and/or boundary value problems for isometric immersions in $\R^3$. The compensated compactness framework formed here is a natural formulation to ensure the weak continuity of the Gauss-Codazzi system for approximate solutions, which yields the isometric realization of two-dimensional surfaces in $\R^3$. As a first application of this approach, we study the isometric immersion problem for two-dimensional Riemannian manifolds with strictly negative Gauss curvature. We prove that there exists a $C^{1,1}$ isometric immersion of the two-dimensional manifold in $\R^3$ satisfying our prescribed initial conditions. TComment: 25 pages, 6 figue

Composite cathode La0.4Sr0.4TiO3-[delta]- Ce0.8Sm0.2O2-[delta] impregnated with Ni for high-temperature steam electrolysis

Composite Ni–SDC (Samaria doped Ceria) cathodes are able to operate in strong reducing atmospheres for steam electrolysis, and composite cathodes based on redox-stable La0.4Sr0.4TiO3 (LSTO) have demonstrated promising performances without the reducing gas flow. However, the electro-catalytic activity of cathodes based on LSTO is insufficient for the efficient electrochemical reduction of steam or carbon oxide. In this work, catalytic-active Ni nanoparticles were loaded on a La0.4Sr0.4TiO3−δ–Ce0.8Sm0.2O2−δ cathode (Ni-loaded LSTO–SDC) via an impregnation method to improve the electrode performances for direct steam electrolysis. The synergetic effect of catalytically-active Ni nanoparticles and the redox-stable LSTO–SDC skeleton contributed to the improved performances and the excellent stability of the cathode for direct steam electrolysis. The current efficiency with a Ni-loaded cathode was enhanced by 3% and 17% compared to the values with a bare LSTO–SDC cathode under 2.0 V of applied voltage at 800 °C with a flow of 3% H2O/5% H2/Ar and 3% H2O/Ar to cathodes, respectively