Related papers: Linear stability analysis of capillary instabiliti…
In this article we study the local stabilization of the non-homogeneous Navier- Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that…
We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $\nu$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with…
We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…
We study the stability of the Kolmogorov flows which are stationary solutions to the two-dimensional Navier-Stokes equations in the presence of the shear external force. We establish the linear stability estimate when the viscosity…
Fluid flows are typically studied by solving the Navier--Stokes equation. One of the fundamental assumptions of this equation is Stokes' hypothesis. This hypothesis assumes bulk viscosity, to be identically zero. The Stokes' hypothesis is a…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
This work is devoted to the global existence of weak solution for a general isothermal model of capillary fluids derived by C. Rohde, which can be used as a phase transition model. This article is structured in the following way: first of…
The Navier-Stokes-Voigt (NSV) model of viscoelastic incompressible fluid has been recently proposed as a regularization of the 3D Navier-Stokes equations for the purpose of direct numerical simulations. In this work we investigate its…
We study the drainage of a viscous liquid film coating outside a horizontal cylinder. We first study the evolution of the axially invariant draining flow, initiated at rest with uniform film thickness $\delta$. Non-linear simulations…
It is known that scale invariance is broken in the developed hydrodynamic turbulence due to intermittency, substantiating complexity of turbulent flows. Here we challenge the concept of broken scale invariance by establishing a hidden…
We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of…
Primary instability of the lid-driven flow in a cube is studied by a comprehensive linear stability approach. Two cases, in which the lid moves parallel to the cube sidewall or parallel to the diagonal plane, are considered. The SIMPLE…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
We study the sedimentation of U-shaped circular disks in the Stokes limit of vanishing inertia. We simulate the flow past such disks using a finite-element-based solution of the 3D Stokes equations, accounting for the integrable…
In this article we study three capillary compressible models (the classical local Navier-Stokes-Korteweg system and two non-local models) for large initial data, bounded away from zero, and with a reference pressure state $\bar{\rho}$ which…
We analyse the buckling stability of a thin, viscous sheet when subject to simple shear, providing conditions for the onset of the dominant out-of-plane modes using two models: (i) an asymptotic theory for the dynamics of a viscous plate…
We prove a stability threshold theorem for 2D Navier-Stokes on three unbounded domains: the whole plane $\mathbb{R} \times \mathbb{R}$, the half plane $\mathbb{R} \times [0,\infty)$ with Navier boundary conditions, and the infinite channel…
We model multi-dimensional two-phase flows of incompressible fluids in porous media using generalized Forchheimer equations and the capillary pressure. Firstly, we find a family of steady state solutions whose saturation and pressure are…
We present a symmetry classification of the linearised Navier-Stokes equations for a two-dimensional unbounded linear shear flow of an incompressible fluid. The full set of symmetries is employed to systematically derive invariant ansatz…
We consider a non-Newtonian fluid flow in a thin domain with thickness $\eta_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear…