Asymptotic Behavior of a Viscous Liquid-Gas Model with Mass-Dependent Viscosity and Vacuum

In this paper, we consider two classes of free boundary value problems of a viscous two-phase liquid-gas model relevant to the flow in wells and pipelines with mass-dependent viscosity coefficient. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. We obtain the asymptotic behavior and decay rates of the mass functions $n(x,t)$,\$m(x,t)$ when the initial masses are assumed to be connected to vacuum both discontinuously and continuously, which improves the corresponding result about Navier-Stokes equations in \cite{Zhu}.Comment: 24 page

Joint Trajectory and Communication Design for UAV-Enabled Multiple Access

Unmanned aerial vehicles (UAVs) have attracted significant interest recently in wireless communication due to their high maneuverability, flexible deployment, and low cost. This paper studies a UAV-enabled wireless network where the UAV is employed as an aerial mobile base station (BS) to serve a group of users on the ground. To achieve fair performance among users, we maximize the minimum throughput over all ground users by jointly optimizing the multiuser communication scheduling and UAV trajectory over a finite horizon. The formulated problem is shown to be a mixed integer non-convex optimization problem that is difficult to solve in general. We thus propose an efficient iterative algorithm by applying the block coordinate descent and successive convex optimization techniques, which is guaranteed to converge to at least a locally optimal solution. To achieve fast convergence and stable throughput, we further propose a low-complexity initialization scheme for the UAV trajectory design based on the simple circular trajectory. Extensive simulation results are provided which show significant throughput gains of the proposed design as compared to other benchmark schemes.Comment: Submitted for possible publicatio