Abstract: In this paper, we establish existence of global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles by combining variational method, various elliptic estimates and a compensated compactness method. More precisely, it is shown that there exist global subsonic flows in nozzles for incoming mass flux less than a critical value; moreover, uniformly subsonic...

A compensated compactness framework is established for sonic-subsonic approximate solutions to the two-dimensional Euler equations for steady irrotational flows that may contain stagnation points. Only crude estimates are required for establishing compactness. It follows that the set of subsonic irrotational solutions to the Euler equations is compact; thus flows with sonic points over an obsta...

We prove the ellipticity principle for selfsimilar potential flows for gas dynamics. We show that the interior of a pseudo-subsonic-sonic-region of a smooth solution must be pseudo-subsonic. In fact, the pseudo-Mach number is below that of a domain-dependent function which is < 1 in the interior and ≤ 1 on the boundary. Therefore the interior must stay pseudo-subsonic under homotopy of pseudo-s...

We follow the approach used by Davies and Pringle (1981) and discuss the trans-sonic substage of the propeller regime. This substage is intermediate between the supersonic and subsonic propeller substages. In the trans-sonic regime an envelope around a magnetosphere of a neutron star passes through a kind of a reorganization process. The envelope in this regime consists of two parts. In the bot...

[1] The Titan-Saturn plasma interaction is studied using a global numerical kinetic model. The developed selfconsistent three-dimensional quasi-neutral hybrid model is used to study Titan’s interaction with supersonic and subsonic plasma flow. The subsonic flow case represents Titan in the Kronian magnetosphere during the Voyager-1 flyby. The supersonic and weakly supermagnetosonic flow cases a...

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the n-dimensional(n ≥ 2) Euler equations for steady irrotational flow that may contain stagnation points. This compactness framework holds provided that the approximate solutions are uniformly bounded and satisfy H−1 loc (Ω) compactness conditions. As illustration, we show the existence...

In this paper, we construct various special solutions on a convergent-divergent surface for the steady compressible complete Euler system and established the stability of the purely subsonic flows. For a given pressure p0 prescribed at the “entry” of the surface, as the pressure p1 at the “exit” decreases, the flow patterns on the surface change continuously as those happen in a de Laval nozzle...

We consider the Saint-Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic stead...