Related papers: A Liouville theorem for the Euler equations in a d…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
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…
We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…
In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady Euler flows with helical symmetry, such that the associated…
For any positive integer $k$, we prove the existence of nontrivial $C^k$-smooth uniformly rotating solutions to the 2D incompressible Euler equations with compact spatial support. These solutions, which can be chosen to be small…
We consider the incompressible axisymmetric Navier-Stokes equations with swirl as an idealized model for tornado-like flows. Assuming an infinite vortex line which interacts with a boundary surface resembles the tornado core, we look for…
We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain $[0,2\pi)\times[0,2\pi / \kappa)$ for $\kappa\in\mathbb{R}^+$, the Euler equations admit a family of stationary…
We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992). The domains we consider have a boundary…
We consider the flow of an { ideal} fluid in a 2D-bounded domain, admitting flows through the boundary of this domain. The flow is described by Euler equations with \textit{non-homogeneous } Navier slip boundary conditions. These conditions…
In this paper we study Liouville properties of smooth steady axially symmetric solutions of the Navier-Stokes equations. First, we provide another version of the Liouville theorem of \cite{kpr15} in the case of zero swirl, where we replaced…
The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
The nonlinear asymptotic stability of shear flows in the 2D Euler equations has traditionally been linked to inviscid damping in the periodic setting. Since Gevrey regularity is required to suppress the ``echo'' phenomenon, asymptotic…
This paper investigates an incompressible steady free boundary problem of Euler equations with helical symmetry in $3$ dimensions and with nontrivial vorticity. The velocity field of the fluid arises from the spiral of its velocity within a…
We prove that any steady solution to the real analytic Euler equations on a Riemannian 3-sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable…
We consider a steady axisymmetric solution of the Euler equations for a fluid (incompressible and with zero vorticity) with a free surface, acted on only by gravity. We analyze stagnation points as well as points on the axis of symmetry. At…
We show that, in a two-dimensional (2d) ideal fluid (also applies to a column of quasi-2d non-neutral plasma in an axial magnetic field), large elliptical vortices in a finite disk are stable. The stability is established by comparison…
The 2D Euler system, which governs inviscid incompressible fluid flow, can admit infinitely many steady solutions in a given domain with slip boundary conditions. To select physical classical solutions, we investigate the vanishing…
We consider solutions of the 2-d compressible Euler equations that are steady and self-similar. They arise naturally at interaction points in genuinely multi-dimensional flow. We characterize the possible solutions in the class of flows…
In this paper, we investigate the 3D inhomogeneous Navier-Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution $(\rho, \mathbf{u})$ satisfies suitable conditions.