Related papers: Vortex dynamics on a M\"obius strip
A classical model for sources and sinks in a two-dimensional perfect incompressible fluid occupying a bounded domain dates back to Yudovich in 1966. In this model, on the one hand, the normal component of the fluid velocity is prescribed on…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we…
In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and…
The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is highly oscillating in time, the corresponding Euler flow cannot keep the…
The nonequilibrium dynamics of vortices in 2D quantum fluids can be predicted by accounting for the way in which vortex ellipticity is coupled to the gradient in background fluid density. In the absence of nonlinear interactions, a…
In this paper we consider steady vortex flows for the incompressible Euler equations in a planar bounded domain. By solving a variational problem for the vorticity, we construct steady double vortex patches with opposite signs concentrating…
In this paper, we are concerned with nonlinear desingularization of steady vortex rings of three-dimensional incompressible Euler fluids. We focus on the case when the vorticity function has a simple discontinuity, which corresponding to a…
Quantized vortices are the prototypical feature of superfluidity. Pervasive in all natural systems, vortices are yet to be observed in dipolar quantum gases. Here, we exploit the anisotropic nature of the dipole-dipole interaction of a…
The boundary conditions prescribing the constant traction or the so-called do-nothing conditions are frequently taken on artificial boundaries in the numerical simulations of steady flow of incompressible fluids, despite the fact that they…
In steady-state non-isentropic flows of perfect fluids there is always thermodynamic generation of vorticity when the difference between the product of the temperature with the gradient of the entropy and the gradient of total enthalpy is…
Fractional Navier-Stokes equations -- featuring a fractional Laplacian -- provide a `bridge' between the Euler equations (zero diffusion) and the Navier-Stokes equations (full diffusion). The problem of whether an initially smooth flow can…
We study the Euler equations describing the motion of an incompressible fluid on the cubic torus with real initial data. We construct solutions on the Fourier side which display a sudden loss of regularity within finite time even for highly…
In Part I of the paper, we prove non-uniqueness of the solution to the Cauchy problem of the Euler equations of an ideal incompressible fluid in dimension two with vorticity in some Lebesgue space. The radially symmetric external force is…
We revisit the boundary dynamics of asymptotically flat, three dimensional gravity. The boundary is governed by a momentum conservation equation and an energy conservation equation, which we interpret as fluid equations, following the…
Smooth solutions of the forced incompressible Euler equations satisfy an energy balance, where the rate-of-change in time of the kinetic energy equals the work done by the force per unit time. Interesting phenomena such as turbulence are…
We construct infinitely many admissible weak solutions to the 2D incompressible Euler equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a simple closed curve in a suitable H\"older space and the…
We show that a certain class of vortex blob approximations for ideal hydrodynamics in two dimensions can be rigorously understood as solutions to the equations of second-grade non-Newtonian fluids with zero viscosity, and initial data in…
Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a…