Related papers: Three-dimensional structural stability of shock wa…
In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions. Non-existence result is…
The goal of this paper is to prove the existence and stability of shocks for viscous scalar conservation laws with space periodic flux, in the multi-dimensional case. Such a result had been proved by the first author in one space dimension,…
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly…
We study viscous-dispersive shock waves with infinite oscillations of the Korteweg-de Vries-Burgers (KdVB) equation. First, we establish detail structures of the shock waves, including the rates at which the local extrema converge to the…
A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge selective surface (electric membrane, electrode, or system of micro-/nanochannels) is carried out and analyzed. A special finite-difference…
We treat the 1D shock tube problem, establishing existence of steady solutions of full (nonisentropic) polytropic gas dynamics with arbitrary noncharacteristic data. We present also numerical experiments indicating uniqueness and…
We examine the stability of an Einstein-Maxwell perfect fluid configuration with a privileged direction of symmetry by means of a $1+1+2$-tetrad formalism. We use this formalism to cast, in a quasi linear symmetric hyperbolic form the…
In this paper, the asymptotic-time behavior of solutions to an initial boundary value problem in the half space for 1-D isentropic Navier-Stokes system is investigated. It is shown that the viscous shock wave is stable for an impermeable…
(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 forced-vibration response of a simply-supported isotropic thick-walled hollow elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surfaces is studied within the framework of linear…
Extending recent results in the isentropic case, we use a combination of asymptotic ODE estimates and numerical Evans-function computations to examine the spectral stability of shock-wave solutions of the compressible Navier--Stokes…
We are concerned with nonlinear stability and existence of two-dimensional current-vortex sheets in ideal compressible magnetohydrodynamics. This is a nonlinear hyperbolic initial-boundary value problem with characteristic free boundary. It…
We extend the Kreiss--Majda theory of stability of hyperbolic initial--boundary-value and shock problems to a class of systems, notably including the equations of magnetohydrodynamics (MHD), for which Majda's block structure condition does…
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and…
We establish nonlinear $H^2\cap L^1 \to H^2$ stability with sharp rates of decay in $L^p$, $p\geq 2$, of general hydraulic shock profiles, with or without subshocks, of the inviscid Saint-Venant equations of shallow water flow, under the…
We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant…
I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…
We establish the global existence and stability of a three-dimensional supersonic conic shock wave for a perturbed steady supersonic flow past an infinitely long circular cone with a sharp angle. The flow is described by a 3-D steady…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
A technique for developing convex dual variational principles for the governing PDE of nonlinear elastostatics and elastodynamics is presented. This allows the definition of notions of a variational dual solution and a dual solution…