A hyperbolic system and the cost of null controllability for the Stokes system

This paper is devoted to study the cost of the null controllability for the Stokes system. Using the control transmutation method we show that the cost of driving the Stokes system to rest at time T is of order e^C/T when T -->0^+,i.e., the same order as for the heat equation. For this to be possible, we are led to study the exact controllability of one hyperbolic system with a resistance term, which will be done under assumptions on the control region.Comment: 17 page

A uniform controllability result for the Keller-Segel system

In this paper we study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic system when the control is acting on the component of the chemical

High Latitude HI in NGC 2613: Buoyant Disk-Halo Outflow

We combine new VLA D array HI data of NGC 2613 with previous high resolution data to show new disk-halo features in this galaxy. The global HI distribution is modeled in detail using a technique which can disentangle the effects of inclination from scale height and can also solve for the average volume density distribution in and perpendicular to the disk. The model shows that the galaxy's inclination is on the low end of the range given by Chaves & Irwin (2001) and that the HI disk is thin (z_e = 188 pc), showing no evidence for halo. Numerous discrete disk-halo features are observed, however, achieving z heights up to 28 kpc from mid-plane. One prominent feature in particular, of mass, 8X10^7 Msun and height, 22 kpc, is seen on the advancing side of the galaxy at a projected galactocentric radius of 15.5 kpc. If this feature achieves such high latitudes because of events in the disk alone, then input energies of order ~ 10^{56} ergs are required. We have instead investigated the feasibility of such a large feature being produced via buoyancy (with drag) within a hot, pre-existing X-ray corona. Reasonable plume densities, temperatures, stall height (~ 11 kpc), outflow velocities and ages can indeed be achieved in this way. The advantage of this scenario is that the input energy need only be sufficient to produce blow-out, a condition which requires a reduction of three orders of magnitude in energy. If this is correct, there should be an observable X-ray halo around NGC 2613.Comment: 32 pages 7 gif figures, accepted by Ap