From the dynamics of gaseous stars to the incompressible Euler equations

Abstract

A model for the dynamics of gaseous stars is introduced and formulated by the Navier-Stokes-Poisson system for compressible, reacting gases. The combined quasineutral and inviscid limit of the NavierStokes-Poisson system in the torus T n is investigated. The convergence of the Navier-Stokes-Poisson system to the incompressible Euler equations is proven for the global weak solution and for the case of general initial data.

On a nonlinear model for tumour growth with drug application

“…By using (5.13) we have that for any text function ϕ. Now in the same spirit of [8] we can let ω → 0 in the weak formulations (6.8), (6.14), (6.15) and we complete the proof of Theorem 2.2.…”

Inviscid incompressible limit for the strong stratified flow of a chemically reacting gaseous mixture

“…Note that the scalings of d ε , κ ε are motivated by [3,7]. Assume that the initial data have the following property at infinity:…”

“…on [0, T * ), see Donatelli and Trivisa [3]. The outline of this article is as follows: In Section 2 we present the rigorous result for (1.8) and (1.9), and in Section 3 we give the proof of the main result for the compressible flow of chemically reacting gaseous mixture (1.4)-(1.6).…”

Low Mach number limit for the quantum hydrodynamics system

“…Then, in the case of an unbounded domain (whole or exterior domain) we can observe that the acoustic waves redistribute their energy in the space and so one can exploit the dispersive properties of these waves to get the local decay of the acoustic energy and to recover compactness in time, see for example [5], [7], [8], [13]. In the case of a periodic domain we don't have a dispersion phenomenon but the waves interact with each other, so in the spirit of Schochet [28] and [29] one has to introduce an operator which describes the oscillations in time so that they can be included in the energy estimates, see [25], [26], [15], [22]. In this paper we will study the incompressible limit in a periodic domain for the system of quantum hydrodynamics (7) and, as explained above, the main issue is to control the time oscillations of the density fluctuation and of the momentum J ε .…”