Related papers: Dynamics of Ideal Fluid Flows
Turbulent flows of incompressible liquid in two dimensions are comprised of dense systems of vortices. Such system of vortices can be treated as a fluid and itself could be described in terms of hydrodynamics. We develop the hydrodynamics…
It is nowadays well understood that the multidimensional isentropic Euler system is desperately ill--posed. Even certain smooth initial data give rise to infinitely many solutions and all available selection criteria fail to ensure both…
In this paper, we establish two stability theorems for steady or traveling solutions of the two-dimensional incompressible Euler equation in a finite periodic channel, extending Arnold's classical work from the 1960s. Compared to Arnold's…
Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in applications, and their leading-order behavior can be described by the hydrostatic Euler…
In this paper we study the inhomogeneous incompressible Euler equations in the whole space $\mathbb{R}^n$ with $n\geq3$. We obtain well-posedness and blow-up results in a new framework for inhomogeneous fluids, more precisely Besov-Herz…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
This manuscript concerns the dynamical interactions between wind and water waves, which are characterized through two-phase free interface problems for the Euler equations. We provide a comprehensive derivation on the linearized problems of…
We obtain a complete solution to the problem of classifying all two-dimensional ideal fluid flows with harmonic Lagrangian labelling maps; thus, we explicitly provide all solutions, with the specified structural property, to the…
We assert that the solutions to the Cauchy problem of the inviscid vorticity equation remain regular and unique for any smooth initial data of finite energy. However, the primitive formulation of the Euler equations is not well-posed, due…
We study the finite element formulation of general boundary conditions for incompressible flow problems. Distinguishing between the contributions from the inviscid and viscid parts of the equations, we use Nitsche's method to develop a…
We study the interaction between the stability, and the propagation of regularity, for solutions to the incompressible 3D Euler equation. It is still unknown whether a solution with smooth initial data can develop a singularity in finite…
This work is devoted to the long-standing open problem of homogenization of 2D perfect incompressible fluid flows, such as the 2D Euler equations with impermeable inclusions modeling a porous medium, and such as the lake equations. The main…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
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 two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
We are concerned with the formation of singularities and the existence of global continuous solutions of the Cauchy problem for the one-dimensional non-isentropic Euler equations for compressible fluids. For the isentropic Euler equations,…
We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity…
We give a survey of recent results on weak-strong uniqueness for compressible and incompressible Euler and Navier-Stokes equations, and also make some new observations. The importance of the weak-strong uniqueness principle stems, on the…
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…