A problem in Rayleigh-Taylor instability
An analysis of stability concepts for the Navier-Stokes equations.
An optimal viscosity profile in the secondary oil recovery
Asymptotic stability of Oseen vortices for a density-dependent incompressible viscous fluid
Asymptotic stability theorems for viscous fluid motions in exterior domains
Dense Granular Poiseuille Flow
We consider a dense granular shear flow in a two-dimensional system. Granular systems (composed of a large number of macroscopic particles) are far from equilibrium due to inelastic collisions between particles: an external driving is needed to maintain the motion of particles. Theoretical description of driven granular media is especially challenging for dense granular flows. This paper focuses on a gravity-driven dense granular Poiseuille flow...
Elliptic quasi-variational inequalities and application to a non-stationary problem in hydraulics
Global existence and one-dimensional nonlinear stability of shearing motions of viscoelastic fluids of Oldroyd type
Modulational stability of Korteweg-de Vries and Boussinesq wavetrains.
On the -instability and -controllability of steady flows of an ideal incompressible fluid
In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...
On The Plane Creeping Flow Of Second Order Fluids With Mixed Boundary Conditions
On the plane creeping flow of second order fluids with mixed boundary conditions.
On the Stability of Bilinear-Constant Velocity-Pressure Finite Elements.
Stability and bifurcation in viscous incompressible fluids
Stability and instability in nineteenth-century fluid mechanics
The stability or instability of a few basic flows was conjectured, debated, and sometimes proved in the nineteenth century. Motivations varied from turbulence observed in real flows to permanence expected in hydrodynamic theories of matter. Contemporary mathematics often failed to provide rigorous answers, and personal intuitions sometimes gave wrong results. Yet some of the basic ideas and methods of the modern theory of hydrodynamic instability occurred to the elite of British and German mathematical...
Sur la stabilisation des fluides parfaits incompressibles bidimensionnels
Некорректность нелинейной задачи о развитии неустойчивости Тейлора
Нестационарное кавитационное обтекание контура в канале
О нелинейных уравнениях переменного типа