相关论文: On the Mach stem configuration with shallow angle
We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
The linear stability with variable coefficients of the vortex sheets for the two-dimensional compressible elastic flows is studied. As in our earlier work on the linear stability with constant coefficients, the problem has a free boundary…
The stability of subcritical perpendicular fast magnetosonic shocks, which are propagating at 1.7 times the fast magnetosonic speed, is investigated using two-dimensional PIC simulations. The plasma, composed of electrons and fully ionized…
Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as…
This paper concerns with the large-time behaviors of the viscous shock profile and rarefaction wave under initial perturbations which tend to space-periodic functions at infinities for the one-dimensional compressible Navier-Stokes-Poisson…
We investigate the effects of ambipolar diffusion and the Hall effect on the stability of weakly-ionized, magnetized planar shear flows. Employing a local approach similar to the shearing-sheet approximation, we solve for the evolution of…
We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced.…
(substantial changes to section 3.2, otherwise minor) We present an analysis of the hydrodynamic stability of a cold slab bounded by two accretion shocks. Previous numerical work has shown that when the Mach number of the shock is large the…
Streamer ionization fronts are pulled fronts propagating into a linearly unstable state; the spatial decay of the initial condition of a planar front selects dynamically one specific long time attractor out of a continuous family. A…
Magnetic buoyancy instability plays an important role in the evolution of astrophysical magnetic fields. Here we revisit the problem introduced by \citet{Gilman_1970} of the short wavelength linear stability of a plane layer of compressible…
The simulation of extreme Mach astrophysical flows is traditionally viewed through the lens of deterministic positivity-preserving schemes. However, due to Kelvin--Helmholtz instabilities and shock anomalies, the multi-dimensional Euler…
We prove the nonlinear stability of the planar viscous shock up to a time-dependent shift for the three-dimensional (3D) compressible Navier-Stokes equations under the generic perturbations, in particular, without zero mass conditions.…
Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow…
In the experiments on stress-induced phase transitions in SMA strips, several interesting instability phenomena have been observed, including a necking-type instability, a shear-type instability and an orientation instability. By using the…
We investigate the Mach number dependence of the radiative overstability of shocks. We find that the stability of radiative shocks increases with decreasing Mach number, with the result that M=2 shocks require cooling exponents < -1.2 to be…
We are concerned with the Prandtl-Meyer reflection configurations of unsteady global solutions for supersonic flow impinging upon a symmetric solid wedge. Prandtl (1936) first employed the shock polar analysis to show that there are two…
In this paper, by means of the Riesz basis approach, we study the stability of a weakly damped system of two second order evolution equations coupled through the velocities. If the fractional order damping becomes viscous and the waves…
We study the stability of Stokes waves on a free surface of an ideal fluid of infinite depth. For small steepness the modulational instability dominates the dynamics, but its growth rate is vastly surpassed for steeper waves by an…
Shocks in granular media, such as vertically oscillated beds, have been shown to develop instabilities. Similar jet formation has been observed in explosively dispersed granular media. Our previous work addressed this instability by…