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We consider by a combination of analytical and numerical techniques some basic questions regarding the relations between inviscid and viscous stability and existence of a convex entropy. Specifically, for a system possessing a convex…
We reconsider the radial Saffman-Taylor instability, when a fluid injected from a point source displaces another fluid with a higher viscosity in a Hele-Shaw cell, where the fluids are confined between two neighboring flat plates. The…
In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $\nu>0$ in $\mathbb{T}\times\mathbb{R}$. It's generally known the nonlinear asymptotic stability…
A recent experiment showed that cylindrical segments of water filling a hydrophilic stripe on an otherwise hydrophobic surface display a capillary instability when their volume is increased beyond the critical volume at which their apparent…
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines computation of the stability eigenvalues and direct…
We report on an instability arising when surface gravity waves propagate in a rotating frame. The Stokes drift associated to the uniform wave field, together with global rotation, drives a mean flow in the form of a horizontally invariant…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…
It is well-established that shear flows in a periodic strip are linearly unstable for the incompressible Navier Stokes equations provided the viscosity is small enough. In this article, under a natural spectral assumption which is satisfied…
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and…
Within the framework of shallow-water magnetohydrodynamics, we investigate the linear instability of horizontal shear flows, influenced by an aligned magnetic field and stratification. Various classical instability results, such as…
The ability to control wettability is important for a wide range of technological applications in which precise microfluidic handling is required. It is known that predesigned roughness at a micro- or nano- scale enhances the wetting…
We use the Maslov index to study the spectrum of a class of linear Hamiltonian differential operators. We provide a lower bound on the number of positive real eigenvalues, which includes a contribution to the Maslov index from a non-regular…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
Three-dimensional direct numerical simulations of an incompressible open square cavity flow are conducted. Features of the permanent (non-linear) regime together with the linear stability analysis of a two-dimensional steady base flow are…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary…
Two-dimensional (2D) flows are efficiently controlled with spanwise waviness, i.e. spanwise-periodic (SP) wall blowing/suction/deformation. We tackle the global linear stability of 2D flows subject to small-amplitude 3D SP control. Building…
The stability of the flux line lattice has been investigated within anisotropic London theory. This is the first full-scale investigation of instabilities in the `chain' state. It has been found that the lattice is stable at large fields,…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
In the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms \begin{equation*}…