Related papers: Instability of strong regular reflection and count…
The Global Magnetorotational Instability (MRI) is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…
It has been shown recently that spectral flow admits a natural integer-valued extension to essential spectrum. This extension admits four different interpretations; two of them are singular spectral shift function and total resonance index.…
We prove that if a rescaled mean curvature flow is a global graph over the round cylinder with small gradient and converges super-exponentially fast, then it must coincide with the cylinder itself. We also show that the result is sharp with…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
We show that for steady compressible potential flow in a class of straight divergent nozzles with arbitrary cross-section, if the flow is supersonic and spherically symmetric at the entry, and the given pressure (velocity) is appropriately…
Linear eigenmodes of a spherically symmetrical ultra-relativistic blast wave (the Blandford-McKee, BMK, solution) are calculated. The BMK solution is shown to be stable and strongly non-universal. It is stable because all the eigenmodes…
The recent discovery of unstable travelling waves (TWs) in pipe flow has been hailed as a significant breakthrough with the hope that they populate the turbulent attractor. We confirm the existence of coherent states with internal fast and…
We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients. It is shown that the standard magnetorotational instability, (MRI) criterion drawn from the local dispersion…
We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background…
In this paper we study continuous parametrized families of dissipative flows, which are those flows having a global attractor. The main motivation for this study comes from the observation that, in general, global attractors are not robust,…
The turbulent boundary layer scaling parameters for the velocity profile are usually associated with either the inner viscous region or the outer boundary layer region. It has been a long-held view that complete similarity of the velocity…
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not…
Regular reflection (RR) to Mach reflection(MR) transitions (RR-MR) on long wedges in steady supersonic flows have been well studied and documented. However, in a short wedge where the wedge length is small, the transition prediction becomes…
Shock waves are steep wave fronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how…
We consider the long-time behavior of irrotational solutions of the three-dimensional compressible Euler equations with shocks, hypersurfaces of discontinuity across which the Rankine-Hugoniot conditions for irrotational flow hold. Our…
We establish a weak-strong uniqueness principle for solutions to entropy-dissipating reaction-diffusion equations: As long as a strong solution to the reaction-diffusion equation exists, any weak solution and even any renormalized solution…
The existence and stability of a spherical transonic shock in a hemispherical shell under the three dimensional perturbations of the incoming flows and the exit pressure is established without any further restrictions on the background…
Reflection of a normal incident matter wave by a perfectly reflecting wall moving with a constant velocity is investigated. A surprising phenomenon is found-that if the the wall moves faster than the phase velocity of the incident wave,…
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…