Transonic Shocks In Multidimensional Divergent Nozzles

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure. The proof is based on solving a free boundary problem for a system of partial differential equations consisting of an elliptic equation and a transport equation. In the process, we obtain unique solvability for a class of transport equations with velocity fields of weak regularity(non-Lipschitz), an infinite dimensional weak implicit mapping theorem which does not require continuous Frechet differentiability, and regularity theory for a class of elliptic partial differential equations with discontinuous oblique boundary conditions.Comment: 54 page

Stability Of contact discontinuity for steady Euler System in infinite duct

In this paper, we prove structural stability of contact discontinuities for full Euler system

Detection of X-ray-Emitting Hypernova Remnants in M101

Based on an ultra deep (230 ks) ROSAT HRI imaging of M101, we have detected 5 X-ray sources that coincide spatially with optical emission line features previously classified as supernova remnants in this nearby galaxy. Two of these coincidences (SNR MF83 and NGC5471B) most likely represent the true physical association of X-ray emission with shock-heated interstellar gas. MF83, with a radius of ~ 134 pc, is one of the largest remnants known. NGC5471B, with a radius of 30 pc and a velocity of at least 350 km/s (FWZI), is extremely bright in both radio and optical. The X-ray luminosities of these two shell-like remnants are $\sim 1$ and $3 \times 10^{38} ergs/s$ (0.5-2 keV), about an order of magnitude brighter than the brightest supernova remnants known in our Galaxy and in the Magellanic Clouds. The inferred blastwave energy is $\sim 3 \times 10^{52} ergs$ for NGC5471B and $\sim 3 \times 10^{53}$ ergs for MF83. Therefore, the remnants likely originate in hypernovae, which are a factor of $\gtrsim 10$ more energetic than canonical supernovae and are postulated as being responsible for Gamma-ray bursts observed at cosmological distances. The study of such hypernova remnants in nearby galaxies has the potential to provide important constraints on the progenitor type, rate, energetics, and beaming effect of Gamma-ray bursts.Comment: 10 pages, 2 gif figures, Accepted for publication in Astrophysical Journal Letter