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 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 ...

In [3, 4, 5], we have developed a new tool called tquasi solutions which approximate in some sense the compressible Navier-Stokes equation. In particular it allows to obtain global strong solution for the compressible Navier-Stokes equations with large initial data on the irrotational part of the velocity (large in the sense that the smallness assumption is subcritical in terms of scaling, it t...

Given a bounded autonomous vector field b : R2 → R2, we study the uniqueness of bounded solutions to the initial value problem for the related transport equation ∂tu + b · ∇u = 0. Assuming that b is of class BV and it is nearly incompressible, we prove uniqueness of weak solutions to the transport equation. The starting point of the present work is the result which has been obtained in [10] (wh...

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeabi...

In this paper we focus on an existence of a weak solution to a system describing a self-propelled motion of a single deformable body in a viscous compressible fluid which occupies a bounded domain in the 3 dimensional Euclidean space. The considered governing system for the fluid is the isentropic compressible Navier-Stokes equation. We prove an existence of a weak solution up to a collision.

We calculate the magnetoconductivity tensor of a 2D electron gas in a 1D periodic potential and quantising magnetic fields. We study the internal structure of the Shubnikov-de Haas peaks and analyse recent experimental results. The electronelectron interaction is accounted for within a screened Hartree-Fock approximation (HFA), which describes both compressible strips and an exchange-enhanced s...

In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...

A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to e...

In this paper we will present an adaptive wavelet scheme to solvethe generalized Stokes problem. Using divergence free wavelets, theproblem is transformed into an equivalent matrix vector system, thatleads to a positive definite system of reduced size for thevelocity. This system is solved iteratively, where the applicationof the infinite stiffness matrix, that is sufficiently compressible,is r...