Run Length Encoding(RLE) is one of the oldest algorithms for data-compression available, a method used for compression of large data into smaller and therefore more compact data. It compresses by looking at the data for repetitions of the same character in a row and storing the amount(called run) and the respective character(called run_value) as target-data. Unfortunately it only compresses wit...

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...

It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are timeasymptotically equivalent on the level of expansion waves. The result is proved using the energy method, mak...

We consider a multidimensional model for the dynamic combustion of compressible reacting fluids formulated by the Navier Stokes equations in Euler coordinates. For the chemical model we consider a one way irreversible chemical reaction governed by the Arrhenius kinetics. The existence of globally defined weak solutions of the Navier-Stokes equations for compressible reacting fluids is establish...

This paper treats the quasilinear evolution equations governing the planar motions of incompressible rods. Since incompressibility is here a 2dimensional phenomenon, a thickness variable enters the governing equations in an essential and novel way. These equations have a mathematical structure strikingly different from that for compressible rods. In contrast to the case for compressible rods, t...

We present the results of three-dimensional simulations of supersonic Euler turbulence with grid resolutions up to 1024 points. Our numerical experiments describe nonmagnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We demonstrate that the inertial range scaling properties of turbulence in this strongly compressible regime deviate substantially ...

We study the asymptotic behavior of compressible isentropic flow through porous medium with general L∞ initial data. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. Recent progress gives a definte answer to this conjectu...