Related papers: On weak stability of shock waves in 2D compressibl…
We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all…
We prove the nonlinear time-asymptotic stability of the composite wave consisting of a planar rarefaction wave and a planar viscous shock for the three-dimensional (3D) compressible barotropic Navier-Stokes equations under generic…
Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that…
We investigate the nonlinear stability of compressible vortex sheet solutions for three-dimensional (3D) isentropic elastic flows. Building upon previous results on the weakly linear stability of elastic vortex sheets [19], we perform a…
We give a perturbative analysis for an infinitesimally thin cylindrical shell composed of counter rotating collisionless particles, originally devised by Apostolatos and Thorne. They found a static solution of the shell and concluded by…
We show uniqueness and stability in $L^2$ and for all time for piecewise-smooth solutions to hyperbolic balance laws. We have in mind applications to gas dynamics, the isentropic Euler system and the full Euler system for a polytropic gas…
Previous experiments have revealed that shock waves in thermally relaxing gases, such as ionizing, dissociating and vibrationally excited gases, can become unstable. To date, the mechanism controlling this instability has not been resolved.…
We are concerned with the large-time behavior of the solution to one-dimensional (1D) cubic non-convex scalar viscous conservation laws. Due to the inflection point of the cubic non-convex flux, the solution to the corresponding inviscid…
(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…
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity…
We develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…
Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…
In this paper, we consider the large time behavior of planar shock wave for 3-D compressible isentropic Navier-Stokes equations (CNS) in half space. Providing the strength of the shock wave and initial perturbations are small, we proved the…
We extend the linear analysis of the drag instability in a 1D perpendicular isothermal C-shock by Gu & Chen to 2D perpendicular and oblique C-shocks in the typical environment of star-forming clouds. Simplified dispersion relations are…
The aim of this article is to explain why similar weak stability criteria appear in both the construction of steady Mach stem configurations bifurcating from a reference planar shock wave solution to the compressible Euler equations, as…
In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schr\"odinger equations with potentials. We show that the standing waves are orbitally stable for all frequencies in the $L^{2}$- subcritical and…
In this paper, we study the asymptotic stability of rarefaction waves for the compressible isentropic Navier-Stokes equations with density-dependent viscosity. First, a weak solution around a rarefaction wave to the Cauchy problem is…
In the present study, we investigated flow structures and properties of elastic turbulence in straight 2D channel viscoelastic fluid flow and tested earlier observations. We discovered self-organized cycling process of weakly unstable…
Extending investigations of Antman & Malek-Madani, Schecter & Shearer, Slemrod, Barker & Lewicka & Zumbrun, and others, we investigate phase-transitional elasticity models of strain-gradient effect. We prove the existence of non-constant…
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid-structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on…