Related papers: 3D Euler about a 2D Symmetry Plane
In this paper, we perform a careful numerical study of nearly singular solutions of the 3D incompressible Euler equations with smooth initial data. We consider the interaction of two perturbed antiparallel vortex tubes which was previously…
A new pseudospectral calculation of collapsing Euler vortices \cite{HouLi06} has called into question the long-term conclusions of singular behavior described earlier in \cite{Kerr93,Kerr05}. This review is designed to: improve the…
We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high-resolution adaptively refined numerical simulations up to 8192^3 mesh points. Geometrical properties of Lagrangian…
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to…
We study the interplay between the local geometric properties and the non-blowup of the 3D incompressible Euler equations. We consider the interaction of two perturbed antiparallel vortex tubes using Kerr's initial condition…
A new rescaling of the vorticity moments and their growth terms is used to characterise the evolution of anti-parallel vortices governed by the 3D Euler equations. To suppress unphysical instabilities, the initial condition uses a balanced…
Motivated by the work on stagnation-point type exact solutions (with infinite energy) of 3D Euler fluid equations by Gibbon et al. (1999) and the subsequent demonstration of finite-time blowup by Constantin (2006) we introduce a…
This work is a companion to [EJE1] and its purpose is threefold: first, we will establish local well-posedness for the axi-symmetric $3D$ Euler equation in the domains $\{(x_1,x_2,x_3) \in \mathbb{R}^3 : x_3^2 \le \mathfrak{c}(x_1^2 +…
We provide numerical evidence for a potential finite-time self-similar singularity of the 3D axisymmetric Euler equations with no swirl and with $C^\alpha$ initial vorticity for a large range of $\alpha$. We employ a highly effective…
Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out…
We consider axisymmetric, swirl-free solutions of the Euler equations in three and higher dimensions, of generalized anti-parallel-vortex-tube-pair-type: the initial scalar vorticity has a sign in the half-space, is odd under reflection…
The goal of this numerical study is to get insight into singular solutions of the two-dimensional (2D) Euler equations for non-smooth initial data, in particular for vortex sheets. To this end high resolution computations of vortex layers…
An example of a solution branch of the three dimensional Euler equation Cauchy problem is constructed which develops a singular velocity component and a singular vorticity component after finite time for some data which have Hoelder…
The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial…
We revisit, both numerically and analytically, the finite-time blowup of the infinite-energy solution of 3D Euler equations of stagnation-point-type introduced by Gibbon et al. (1999). By employing the method of mapping to regular systems,…
In this paper, we numerically study a class of solutions with spiraling singularities in vorticity for two-dimensional, inviscid, compressible Euler systems, where the initial data have an algebraic singularity in vorticity at the origin.…
Let $v$ be a solution of the axially symmetric Euler equations (ASE) in a finite cylinder in $\mathbb{R}^3$. We show that suitable blow-up limits of possible velocity singularity and most self similar vorticity singularity near maximal…
A class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…
By introducing a new averaged quantity with a fast decay weight to perform Sideris's argument (Commun Math Phys, 1985) developed for the Euler Equations, we extend the formation of singularities of classical solution to the 3D Euler…
We prove that the 3-D free-surface incompressible Euler equations with regular initial geometries and velocity fields have solutions which can form a finite-time "splash" (or "splat") singularity first introduced in [9], wherein the…