Vorticity dynamics of the three-dimensional incompressible Euler equations are cast into a
quaternionic representation governed by the Lagrangian evolution of the tetrad consisting of …

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 …

By considering the three-dimensional incompressible Euler equations, a 4-vector ζ is
constructed out of a combination of scalar and vector products of the vorticity ω and the …

We demonstrate that, if a globally smooth virtual circulation-preserving velocity exists,
Kelvin's and Helmholtz's theorems can be extended to some non-ideal flows which are …

New analysis of the scaling structure of a numerical solution of the Euler equations finds that
initially antiparallel vortex tubes collapse into two wings whose cross sections can be …

More than 160 years after their invention by Hamilton, quaternions are now widely used in
the aerospace and computer animation industries to track the orientation and paths of …

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Menu Find a journal Publish with us Track your research Search Cart 1.Home 2.Navier-Stokes …

The study of shear flow steady states has led to a wealth of research in the field of fluid
dynamics. By studying shear flows, we can understand how a fluid behaves and how …

A self-similar solution of the three-dimensional (3d) incompressible Euler equations is
defined by u (x, t)= U (y)/(t^*-t)^ α,\; y= x/(t^*-t)^ β, α, β> 0, where U (y) satisfies α U+ β y ⋅ ∇ …

Localized non-blowup conditions for three-dimensional incompressible Euler flows and related
equations Localized non-blowup conditions for three-dimensional incompressible Euler flows …