We study the 2D incompressible Boussinesq equation without thermal diffusion, and aim to
construct rigorous examples of small scale formations as time goes to infinity. In the viscous …

The m-waves of Kelvin are uniformly rotating patch solutions of the 2D Euler equations with
m-fold rotational symmetry for m≥ 2. For Kelvin waves sufficiently close to the disc, we prove …

We study stability of a spherical vortex introduced by M. Hill in 1894, which is an explicit
solution of the three‐dimensional incompressible Euler equations. The flow is axi‐symmetric …

In this paper, we study nonlinear orbital stability of steady vortex rings without swirl, which
are special global solutions of the three-dimensional incompressible Euler equations. We …

We introduce an active vector system, which generalises both the 3D Euler equations and
the electron–magnetohydrodynamic equations (E–MHD). We may as well view the system …

For the 2D incompressible Euler equations, we establish global-in-time ($ t\in\mathbb {R} $)
stability of vortex quadrupoles satisfying odd symmetry with respect to both axes …

We consider a nonlinear model equation, known as the Localized Induction Equation,
describing the motion of a vortex filament immersed in an incompressible and inviscid fluid …

We study the 2-dimensional incompressible Boussinesq equations without thermal diffusion,
and aim to construct rigorous examples of small scale formations as time goes to infinity. In …

We study systems interpolating between the 3D incompressible Euler and electron–MHD
equations, given by∂ t B+ V⋅∇ B= B⋅∇ V, V=−∇×(− Δ)− a B,∇⋅ B= 0, where B is a time …