Related papers: A uniqueness and stability principle for surface d…
This paper considers two-dimensional steady solitary waves with constant vorticity propagating under the influence of gravity over an impermeable flat bed. Unlike in previous works on solitary waves, we allow for both internal stagnation…
We investigate the interaction of waves with surface flows by considering the full set of conserved quantities, subtle but important surface elevation changes induced by wave packets and by directly considering the necessary forces to…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…
Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…
We introduce and study a one-parameter family of curve diffusion flows with a scale-critical cubic curvature term for closed immersed planar curves. We first classify all closed stationary solutions, showing that they are precisely circles…
A universal theory of linear instabilities in swirling flows, occurring in both natural settings and industrial applications, is formulated. The theory encompasses a wide range of open and confined flows, including spiral isothermal flows…
General stability criterions of two-dimensional inviscid parallel flow are obtained analytically for the first time. First, a criterion for stability is found as $\frac{U''}{U-U_s}>-\mu_1$ everywhere in the flow, where $U_s$ is the velocity…
We study the focusing power nonlinear wave equation with any power, in Minkowski space of any spacetime dimension. We present a complete understanding of the local stability and scattering theory (both in high regularity spaces) for…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…
An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions…
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a…
We describe various aspects of plane wave backgrounds. In particular, we make explicit a simple criterion for singularity by establishing a relation between Brinkmann metric entries and diffeomorphism-invariant curvature information. We…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Landau's criterion for superfluidity is a special case of a broader principle: A moving fluid cannot be stopped by frictional forces if its state of motion is a local minimum of the grand potential. We employ this general thermodynamic…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
Existence and uniqueness are investigated for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial…
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a…