Existence of the axisymmetric weak solution to the 3D isothermal stationary compressible Navier-Stokes equations

In this paper, we construct the axisymmetric weak solutions to the 3D isothermal stationary compressible Navier-Stokes equations on the domain D, where the heat ratio equal 1 and the external force g satisfies certain cancellation conditions. We first establish the compactness assertion of the approximation solutions by assuming the total mass of the fluid is finite, then we exclude the trivial solution via imposing another type of restrictions on the density. To deal with the singularities near the symmetric axis and at the far field, we will derive proper weighted estimates of the L2-norm of the velocity field on the unbounded domain D, which belongs to the critical case of the Sobolev's inequality

Microscopic Characteristics and Modelling of Pedestrian Inflow Process with Inactive Persons

Inflow and outflow processes are common phenomena in daily life. Many types of research have been conducted to study the features of the outflow process, especially in scenarios with a single room or a straight corridor. A few scholars have paid attention to the movement characteristics of pedestrian inflow. Further explorations are still under great demand. In this contribution, a set of pre-conducted experiments are used to analyze the characteristics of the pedestrian inflow process with inactive persons. In these experiments, inactive persons were required to randomly cease within the room, leading to intensive detour behavior of pedestrians. The characteristics are carefully investigated using gradient analysis and curl analysis. To mimic the aforementioned inflow process, static global field is constructed to heuristically navigate a social force based microscopic model. The proposed model can reproduce the self-organized phenomena in the experiments. Our work can help understand the field feature of the pedestrian inflow process with inactive persons. High chaos level areas can be marked out providing practical information for managers

Large-Time Behavior of the 2D Compressible Navier-Stokes System in Bounded Domains with Large Data and Vacuum

The large time behavior of the unique strong solution to the barotropic compressible Navier-Stokes system is studied with large external forces and initial data, where the shear viscosity is a positive constant and the bulk one is proportional to a power of the density. Some uniform estimates on the Lp-norm of the density are established, and then deduce that the density converges to its steady state in Lp-spaces, which transforms the large external force into a small one in some sense. Moreover, to deal with the obstacles brought by boundary, the conformal mapping and the pull back Green function are applied to give a point-wise representation of the effective viscous flux, and then make use of slip boundary conditions to cancel out the singularity.Comment: 55 page

FDS SIMULATIONS OF THE TRANSPORT OF COLD FIREBRANDS IN WIND TUNNEL EXPERIMENTS

In wildland fires, the transport of firebrands is the main reason causing subsequent spot fires. The embers can travel farther than the fire itself and ignite the houses at the wildland urban interface (WUI). We consider previous experiments performed in a wind tunnel and used to characterize the transport of cold particles in a controlled velocity field that corresponds to a turbulent jet in a cross-flow. We perform numerical simulations of these experiments using the Fire Dynamics Simulator (FDS). The simulated jet and cross-wind velocity field are adjusted and tested to match the flow velocities measured in the experiments. The solid particles are simulated using the FDS Lagrangian model and our study includes comparisons between simulated and measured trajectories. The relationship between the particle flying pattern with the wind velocity field is examined