Related papers: Non-minimizing Axially Symmetric Cavity Flow
We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady)…
We study an initial-boundary-value problem for time-dependent flows of heat-conducting viscous incompressible fluids in a system of three-dimensional pipes on a time interval $(0,T)$. Here we are motivated by the bounded domain approach…
A computational study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out for the first time. The problem is formulated in Germano coordinates in two equivalent but different…
Existence and regularity of minimizers in elliptic free boundary problems have been extensively studied in the literature. We initiate the corresponding study of higher critical points by considering a superlinear free boundary problem…
Using the standard symmetry technique for applying boundary conditions for free slip and flat walls with corners will lead to flow leak through the wall near corners (violation of no penetration condition) and a corresponding error in…
We study the general properties of dissipative fluid distributions endowed with hyperbolical symmetry. Their physical properties are analyzed in detail. It is shown that the energy density is necessarily negative and the fluid distribution…
In this paper we study isentropic flow in a curved pipe. We focus on the consequences of the geometry of the pipe on the dynamics of the flow. More precisely, we present the solution of the general Cauchy problem for isentropic fluid flow…
We study the nonhomogeneous boundary value problem for the Navier--Stokes equations of steady motion of a viscous incompressible fluid in a three--dimensional exterior domain with multiply connected boundary. We prove that this problem has…
Flow in channels and ducts with adjoining cavities are common in natural and engineered systems. Here we report numerical and experimental results of 3D confined cavity flow, identifying critical conditions in the recirculating flow…
While some works have investigated the particle trajectories and stagnation points beneath solitary waves with constant vorticity, little is known about the pressure beneath such waves. To address this gap, we investigate numerically the…
In the present paper, microcanonical measures for the dynamics of three dimensional (3D) axially symmetric turbulent flows with swirl in a Taylor-Couette geometry are defined, using an analogy with a long-range lattice model. We compute the…
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that…
Local volume-constrained minimizers in anisotropic capillarity problems develop free boundaries on the walls of their containers. We prove the regularity of the free boundary outside a closed negligible set, showing in particular the…
The flow of a gas through porous medium is considered in the case of pressure dependent permeability. Approximate self-similar solutions of the boundary-value problems are found.
In this paper we study a perturbative approach to the problem of quantization of measures in the plane. Motivated by the fact that, as the number of points tends to infinity, hexagonal lattices are asymptotically optimal from an energetic…
When considering a general system of equations describing the space-time evolution (flow) of one or several variables, the problem of the optimization over a finite period of time of a measure of the state variable at the final time is a…
The initial boundary value problem for the three-dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain. The existence and uniqueness is established for both the local strong solution with large initial…
This article is devoted to the study of certain models for phase transitions involving nonlocal energies. A first part is concerned with to the asymptotic analysis of a system of fractional elliptic equations of Allen-Cahn type as a…
Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of…
Recent numerical simulations of lid-driven cavity flow of a nematic liquid crystal have found dynamical behavior where topological defects rotate about the center of the fluid vortex induced by the lid motion. By considering a simpler…