Related papers: Subsonic flows past a profile with a vortex line a…
In a concurrent work, Villois et al. 2020 reported the evidence that vortex reconnections in quantum fluids follow an irreversible dynamics, namely vortices separate faster than they approach; such time-asymmetry is explained by using…
Tichler proved that a manifold admitting a smooth closed one-form fibers over a circle. More generally a manifold admitting $k$ independent closed one-forms fibers over a torus $T^k$. In this article we explain a version of this…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
In this article, we consider a class of the contact discontinuity for the full compressible Euler equations, namely the entropy wave, where the velocity is continuous across the interface while the density and the entropy can have jumps.…
The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a…
This paper develops the geometry and analysis of the averaged Euler equations for ideal incompressible flow in domains in Euclidean space and on Riemannian manifolds, possibly with boundary. The averaged Euler equations involve a parameter…
We flow a hypersurface in Euclidean space by mean curvature flow with a Neumann boundary condition, where the boundary manifold is any torus of revolution. If we impose the conditions that the initial manifold is compatible and does not…
For unipolar hydrodynamic model of semiconductor device represented by Euler-Poisson equations, when the doping profile is supersonic, the existence of steady transonic shock solutions and C-smooth steady transonic solutions for…
In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit…
We are concerned with rigidity properties of steady Euler flows in two-dimensional bounded annuli. We prove that in an annulus, a steady flow with no interior stagnation point and tangential boundary conditions is a circular flow, which…
We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand the smoothness of what we call the spectral density function…
We prove the existence of a subsonic weak solution $({\bf u}, \rho, p)$ to steady Euler system in a two-dimensional infinitely long nozzle when prescribing the value of the entropy $(= \frac{p}{\rho^{\gamma}})$ at the entrance by a…
We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong…
For the model of a compressible barotropic fluid on a two dimensional rotating Riemmanian manifold we discuss a special class of smooth solutions having a form of a steady non-singular vortex moving with a bearing field. The model can be…
In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…
It is proven that the only incompressible Euler fluid flows with fixed straight streamlines are those generated by the normal lines to a round sphere, a circular cylinder or a flat plane, the fluid flow being that of a point source, a line…
A simplified form of the vorticity equation is derived for arbitrary coordinate systems. The present work unifies and extends the previous findings that vorticity is conserved in planar Euler flow, while in axisymmetric Euler rings it is…
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary…
Wave interference has historically relied on scattering objects placed within the wave domain. Here, we introduce a fundamentally new mechanism: scatterless interference induced by a lattice of subsurface phonon motion beneath a smooth wall…
We study the dynamics of vortices formed in a superfluid film adsorbed on the curved two-dimensional surface of a cone. To this aim, we observe that a cone can be unrolled to a sector on a plane with periodic boundary conditions on the…