We study the time-asymptotic behaviour of solutions to a singular perturbation of the inviscid Burgers problem describing sound propagation in a radiating gas. This radiating gas model exhibits the interesting phenomenon known as metastability that has been first identified for the viscous Burgers equation. Precisely, on an initial time span, that scales linearly in the inverse of the perturbation parameter, we can quantify the L1-distance of the solution to the so-called sharp N-wave solution of the inviscid Burgers problem and to a diffusive N-wave. On a second long-time stage that scales exponentially in the inverse of the perturbation parameter, the solutions still remain close to a diffusive N-wave before finally collapsing into diffusion waves. Besides our analysis of the radiating gas model, we also provide an alternative description of metastability in the viscous Burgers model which, unlike other studies, relies on L1-estimates and does not require the passage to similarity variables.
We consider the emergence of rapidly propagating, exponentially small-amplitude oscillations in the impulsively started fifth-order Korteweg--de Vries equation (KdV5), and demonstrate that these waves originate due to Stokes'phenomenon in a small-time boundary layer. We rescale the problem in time and construct an auxi...
Christopher J. Lustri, S. Chapman, R. Nicotra· 0 citations
We present a formulation for the linear stability of the miscible Rayleigh-Taylor instability, retaining viscosity, Fickian mass diffusion, and non-Boussinesq effects. Rather than adopting the diffusive corrections of Duff, Harlow, and Hirt (1962) or relying on the viscous eigenvalue problem of Chandrasekhar (1961), th...
Marildo Kola, Daniel Israel, Aaron Towne· 0 citations
We establish the time-asymptotic stability of generic Riemann solutions for the one-dimensional Navier-Stokes-Fourier-Korteweg (NSFK) system, which describes the dynamics of viscous, heat-conducting, compressible fluids with internal capillarity. We prove that, for the adiabatic exponent $\gamma\in(1,2]$, the solution...
The Kelvin–Helmholtz instability is a fundamental signature of the natural world, manifesting in phenomena ranging from atmospheric clouds to the iconic turbulence of Jupiter’s Great Red Spot. While the linear dynamics of this instability is well-understood, the ultimate fate of the fluid—the final stationary state to...
R. Pakter, Yan Levin· Journal of Statistical Mecha...· 0 citations
The transport of runaway electrons in chaotic magnetic geometries is an area of active study. Computing the transport from the direct simulation of particle trajectories is computationally expensive. Instead, diffusion models, such as the one by Rechester and Rosenbluth (RR), are often employed to incorporate transport...
Dániel Jánosi, Anikó Horváth, H. Bergström et al.· Plasma Physics and Controlle...· 0 citations
This paper investigates the time-asymptotic stability of the one-dimensional full compressible Navier-Stokes-Poisson equations, assuming that the corresponding quasi-neutral Euler equations admit a generic Riemann solution consisting of a shock, a contact discontinuity, and a rarefaction wave. It is proved that there e...
