Well-posedness and exponential stability of the inhomogeneous anisotropic incompressible Navier-Stokes equation with far-field vacuum in two-dimensional whole space

In this paper, we investigate the well-posedness theory and exponential stability for the inhomogeneous incompressible Navier-Stokes equation with only horizontal dissipative structure. Due to the lack of the vertical dissipative term and appearance of vacuum, it is a highly challenging tricky problem for us to study the well-posedness, stability and large-time behavior problems in two-dimensional whole space. The local-in-time well-posedness theory is successfully established at first because we develop some good estimates for the density and vorticity to control the nonlinear term. Finally, these good estimates of density and vorticity help us to establish the global-in-time well-posedness and exponential stability if the initial velocity is suitable small

Asian CBDCs on the rise: An in-depth analysis of developments and implications

In this paper, we present an in-depth analysis of Central Bank Digital Currencies (CBDCs), focusing on their definition, purpose, design considerations and recent developments. We also delve into the potential advantages of CBDCs for Asia, such as enhancing convenience, precisely quantifying economic metrics, managing anonymity, catalyzing innovation, and promoting financial inclusion. Moreover, we examine how CBDCs can fortify monetary and fiscal policies, ensure safe distribution, reduce costs and combat corruption. We also address the risks associated with CBDC adoption in Asia and explore potential outcomes such as substitution effects, valuation fluctuations, and foreign currency dependence, while highlighting the importance of managing financial imbalances, holdings concentration and public apprehension toward digital currencies

Resistance Switching Behavior in Rectangle-Nano-Pattern SrTiO3 Induced by Simple Annealing.

The tunability of semi-conductivity in SrTiO3 single crystal substrates has been realized by a simple encapsulated annealing method under argon atmosphere. This high temperature annealing-induced property changes are characterized by the transmission spectra, scanning electron microscopy (SEM) and synchrotron-based X-ray absorption (XAS). We find the optical property is strongly influenced by the annealing time (with significant decrease of transmittance). A sub gap absorption at ~427 nm is detected which is attributed to the introduction of oxygen vacancy. Interestingly, in the SEM images, annealing-induced regularly rectangle nano-patterns are directly observed which is contributed to the conducting filaments. The XAS of O K-edge spectra shows the changes of electronic structure by annealing. Very importantly, resistance switching response is displayed in the annealed SrTiO3 single crystal. This suggests a possible simplified route to tune the conductivity of SrTiO3 and further develop novel resistance switching materials