Related papers: Universal dynamics in the onset of a Hagen-Poiseui…
We consider the system of partial differential equations governing two-dimensional flows of a robust class of viscoelastic rate-type fluids with stress diffusion, involving a general objective derivative. The studied system generalizes the…
Internally actuated elastic particles are widely used in biomedical applications. It is imperative to understand the dynamics of such particles in pressure-driven microfluidic devices to manipulate their motion. We analytically examine the…
Quantum self-oscillatory phases are ubiquitous in driven-dissipative systems. Classically, each phase is defined by its flow pattern and how stationary sets organize phase space (e.g. fixed points and limit cycles), with transitions…
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in channel-like domains on a time interval $(0,T)$. For the parabolic system with strong nonlinearities and including the…
In wall-bounded flows, the laminar regime remain linearly stable up to large values of the Reynolds number while competing with nonlinear turbulent solutions issued from finite amplitude perturbations. The transition to turbulence of plane…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
Fluid dynamics induced by periodically forced flow around a cylinder is analyzed computationally for the case when the forcing frequency is much lower than the von K{\'a}rm{\'a}n vortex shedding frequency corresponding to the constant flow…
In this paper, we study the unsteady hydromagnetic flow of a Walter's fluid (Model B') down an open inclined channel of width 2a and depth d under gravity, the walls of the channel being normal to the surface of the bottom under the…
The dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell are studied experimentally, theoretically and by phase-field simulations of the H-S equations. As the central, denser fluid is centrifuged, it forms…
We perform a numerical analysis of superfluid turbulence produced by thermal counterflow in He II by using the vortex filament model. Counterflow in a low aspect ratio channel is known to show the transition from laminar flow to the two…
We perform a linear stability analysis of three-layer radial porous media and Hele-Shaw flows with variable viscosity in the middle layer. A nonlinear change of variables results in an eigenvalue problem that has time-dependent coefficients…
We investigate the Couette-Taylor problem for a steady incompressible viscous fluid in a 3D cylindrical annulus, where one of the two cylinders is still, under both Dirichlet and boundary conditions involving the vorticity that naturally…
We consider the solution to the 2D Navier-Stokes equations around the Poiseuille flow $(y^2,0)$ on $\mathbb{T}\times\mathbb{R}$ with small viscosity $\nu>0$. Via a hypocoercivity argument, we prove that the $x-$dependent modes of the…
We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the…
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…
The displacement of a viscous liquid by air in the narrow gap between two parallel plates - a Hele-Shaw channel - is an exemplar of complex pattern formation. Typically, bubbles or fingers of air propagate steadily at low values of the…
We investigate the instability and stability of specific steady-state solutions of the two-dimensional non-homogeneous, incompressible, and viscous Navier-Stokes equations under the influence of a general potential $f$. This potential is…
We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic…
The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is…
This study considers the linear stability of Poiseuille-Rayleigh-B\'enard flows, subjected to a transverse magnetic field to understand the instabilities that arise from the complex interaction between the effects of shear, thermal…