We study the Cauchy problem for equations describing a viscous compressible and heat-conductive fluid in two dimensions. By imposing weight function to initial density deal with Sobolev embedding critical space, constructing an ad-hoc truncation control quadratic nonlinearity appeared energy equation, we establish local time existence of unique strong solution large...

This study analyses compressible gas flows through microchannels or microtubes, and develops two complete sets of asymptotic solutions. It is a natural extension of the previous work by Arkilic et al. on compressible flows through microchannels. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for the Reynolds and Mach numbers at ...

Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, in which the pressure gradient is nearly balanced by gravitational forces. Aims. We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is de...

In a recent paper, C. Monrozeau et al. [27] analyze the influence of neutron superfluidity on the cooling time of inner crust matter in neutron stars, in the case of a rapid cooling of the core of the star. The model used to describe the evolution of temperature [23] in the star follows Lattimer et al. [23]. It supposes a linear dependence of the specific heat as a function of temperature and a...

In this work we study time asymptotic behavior of solutions of 1-d Compressible Navier-Stokes equations toward solutions of Euler equations that consist of two rarefaction waves separated by a vacuum region. The analysis relies on various energy estimates. 0.1 Summary and the main result Time asymptotic toward rarefaction waves for Compressible Navier-Stokes equations for barotropic fluids was ...

In the present work, we are interested in the direct numerical simulation of the compressible Euler and Navier Stokes equations at low Mach number regime. First, we propose a review of existing work on the subject in order to identify the issues raised by the simulation of in this kind of flow, and the existing relevant solutions. Then, we will test different selected compressible low Mach solv...

We consider the compressible barotropic Navier-Stokes system in one dimension, with a nonmonotonic equation of state. The associated free boundary problem is investigated, and we prove asymptotic properties of the unique globally defined solution for large time. We also make some comments on a related model of quantum fluid describing the dynamics of cold nuclear matter (zero temperature). @ 20...

The distributed-relaxation multigrid and defectcorrection methods are applied to the twodimensional compressible Navier-Stokes equations. The formulation is intended for high Reynolds number applications and several applications are made at a laminar Reynolds number of 10,000. A staggeredgrid arrangement of variables is used; the coupled pressure and internal energy equations are solved togethe...

In order to investigate turbulent phenomena in compressible flows the Variational Multiscale method is used. This method is usually applied to incompressible flows. In a first step, we derive the VMS method for the compressible Navier-Stokes equations. The resulting weak formulation of the flow equations is split into resolved and unresolved scales using multiresolution techniques based on bior...

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.