This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity lacks decaying structure. In fact, we show the existence of uniformly rotating solutions as steady states for the compressible Navier-Stokes equations. By manipulating the conservation law of angular momentum, we establish a suitable Korn's type inequality to control the perturbation and show the asymptotic stability of the uniformly rotating solutions with small angular velocity. In particular, the initial perturbation which preserves the angular momentum would decay exponentially in time and the solution to the Navier-Stokes equations converges to the steady state as time grows up.

We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.

In biological transport mechanisms such as insect respiration and renal filtration, fluid travels along a leaky channel allowing material exchange with systems exterior to the channel. The channels in these systems may undergo peristaltic pumping which is thought to enhance the material exchange. To date, little analytic work has been done to study the effect of pumping on material extraction across the channel walls. In this paper, we examine a fluid extraction model in which fluid flowing through a leaky channel is exchanged with fluid in a reservoir. The channel walls are allowed to contract and expand uniformly, simulating a pumping mechanism. In order to efficiently determine solutions of the model, we derive a formal power series solution for the Stokes equations in a finite channel with uniformly contracting/expanding permeable walls. This flow has been well studied in the case in which the normal velocity at the channel walls is proportional to the wall velocity. In contrast we do not assume flow that is proportional to the wall velocity, but flow that is driven by hydrostatic pressure, and we use Darcy’s law to close our system for normal wall velocity. We incorporate our flow solution into a model that tracks the material pressure exterior to the channel. We use this model to examine flux across the channel-reservoir barrier and demonstrate that pumping can either enhance or impede fluid extraction across channel walls. We find that associated with each set of physical flow and pumping parameters, there are optimal reservoir conditions that maximize the amount of material flowing from the channel into the reservoir.

This paper is concerned with the Cauchy problem of the one-dimensional compressible Navier--Stokes equations with degenerate temperature dependent transport coefficients which satisfy conditions from the consideration in kinetic theory. A result on the existence and uniqueness of a globally smooth nonvacuum solution is obtained provided that the -norm of the initial perturbation) for some positive constant independent of . Here is the adiabatic gas constant. This is a Nishida--Smoller type global solvability result with large data.

A computational method, based on ₁-minimization, is proposed for the problem of link flow correction, when the available traffic flow data on many links in a road network are inconsistent with respect to the flow conservation law. Without extra information, the problem is generally ill-posed when a large portion of the link sensors are unhealthy. It is possible, however, to correct the corrupted link flows accurately with the proposed method under a recoverability condition if there are only a few bad sensors which are located at certain links. We analytically identify the links that are robust to miscounts and relate them to the geometric structure of the traffic network by introducing the recoverability concept and an algorithm for computing it. The recoverability condition for corrupted links is simply the associated recoverability being greater than 1. In a more realistic setting, besides the unhealthy link sensors, small