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We investigate the long-term behavior, as a certain regularization parameter vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic incompressible fluid. We prove the existence of global and exponential attractors of…
This note is a correction to a paper of Cortez, Peskin, Stockie & Varela [SIAM J. Appl. Math., 65(2):494-520, 2004], who studied the stability of a parametrically-forced, circular, elastic fiber immersed in an incompressible fluid in 2D,…
Using a form of modified dispersion relations derived in the context of quantum geometry, we investigate limits set by current observations on potential corrections to Lorentz invariance. We use a phenomological model in which there are…
The stability of two-dimensional buoyancy-driven convection in a vertical porous slot, wherein a plane Couette flow is additionally present, is studied. This complex fluid flow scenario is examined under the influence of Robin-type boundary…
We investigate the standard stable manifold theorem in the context of a partially hyperbolic singu-larity of a vector field depending on a parameter. We prove some estimates on the size of the neighbourhood where the local stable manifold…
In this work, we discuss the long-time behavior of non-rotating quasi-2D viscous flows over topographies. We develop a novel theoretical and numerical framework for the analysis of these flows, derived as a dimensional reduction of the 3D…
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for…
At sufficiently high chemical potential massive relativistic spin one fields condense. This phenomenon leads to the spontaneous breaking of rotational invariance while linking it to the breaking of internal symmetries. We study the relevant…
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…
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response…
In relative locality theories the geometric properties of phase space depart from the standard ones given by the fact that spaces of momenta are linear fibers over a spacetime base manifold. In particular here it is assumed that the…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the…
We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are carried out with the presence of a parameter distinguishing whether the underlying…
The linear marginal instability of an MHD Taylor-Couette flow of infinite vertical extension is considered. For hydrodynamically unstable flows the minimum Reynolds number exists even without a magnetic field, but there are also solutions…
We prove an abstract instability result for an eigenvalue problem with parameter. We apply this criterion to show the transverse linear instability of solitary waves on various examples from mathematical physics.
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
We consider perimeter perturbations of a class of attractive-repulsive energies, given by the sum of two nonlocal interactions with power-law kernels, defined over sets with fixed measure. We prove that there exists curves in the…
In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations if the stochastic approximation process enters the…
The linear stability of buoyant parallel flow in a vertical porous layer with an annular cross-section is investigated. The vertical cylindrical boundaries are kept at different uniform temperatures and they are assumed to be impermeable.…