相关论文: Dynamics of two-dimensional time-periodic Euler fl…

We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus…

The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…

In this paper, we study the well-posedness of classical solutions to a two-phase flow model consisting of the pressureless Euler equations coupled with the isentropic compressible Navier-Stokes equations via a drag forcing term. We consider…

We examine the Euler equations within a simply-connected bounded domain. The dynamics of a single point vortex are governed by a Hamiltonian system, with most of its energy levels corresponding to time-periodic motion. We show that for the…

For a spacetime of odd dimensions endowed with a unit vector field, we introduce a new topological current that is identically conserved and whose charge is equal to the Euler character of the even dimensional spacelike foliations. The…

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…

We show that H\"{o}lder continuous incompressible Euler flows that satisfy the local energy inequality ("globally dissipative" solutions) exhibit nonuniqueness and contain examples that strictly dissipate kinetic energy. The collection of…

Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invades a quiescent region, and the velocity and pressure in its…

We study the large-time behavior of finite-energy weak solutions for the Vlasov-Navier-Stokes equations in a two-dimensional torus. We focus first on the homogeneous case where the ambient (incompressible and viscous) fluid carrying the…

This note is devoted to the linear stability of the Couette flow for the non-isentropic compressible Euler equations in a domain $\mathbb{T}\times \mathbb{R}$. Exploiting the several conservation laws originated from the special structure…

In a recent paper, a continuum theory of immiscible and incompressible two-phase flow in porous media based on generalized thermodynamic principles was formulated (Transport in Porous Media, 125, 565 (2018)). In this theory, two immiscible…

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…

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…

A stochastic Euler equation is proposed, describing the motion of a particle density, forced by the random action of virtual photons in vacuum. After time averaging, the Euler equation is reduced to the Reynolds equation, well studied in…

A principle of maximum entropy is proposed in the context of viscous incompressible flow in Eulerian coordinates. The relative entropy functional, defined over the space of $L^2$ divergence-free velocity fields, is maximized relative to…

In this paper, we investigate nonlinear stability of planar steady Euler flows related to least energy solutions of the Lane-Emden equation in a smooth bounded domain. We prove the orbital stability of these flows in terms of both the $L^s$…

The superfluid phase transition of the general vortex gas, in which the circulations may be any non-zero integer, is studied. When the net circulation of the system is not zero the absence of a superfluid phase is shown. When the net…

We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…

In this paper we establish the short-time existence and uniqueness theorem for hyperbolic geometric flow, and prove the nonlinear stability of hyperbolic geometric flow defined on the Euclidean space with dimension larger than 4. Wave…

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…