In this paper, we prove the existence of locally non-radial solutions to the stationary 2D Euler
equations with compact support but non-concentrated around one or several points. Our …

We prove the existence of nonradial classical solutions to the 2D incompressible Euler
equations with compact support. More precisely, for any positive integer $ k $, we construct …

In this paper we reveal the existence of a large family of new, nontrivial and smooth traveling
waves for the 2D Euler equation at an arbitrarily small distance from the Couette flow in H s …

In this paper we consider the incompressible 2D Euler equation in an annular domain with
non-penetration boundary condition. In this setting, we prove the existence of a family of non …

In this paper, we show that the only solution of the vortex sheet equation, either stationary or
uniformly rotating with negative angular velocity Ω Ω, such that it has positive vorticity and is …

V-states are uniformly rotating vortex patches of the incompressible 2D Euler equation and
the only known explicit examples are circles and ellipses. In this paper, we prove the …

We construct co-rotating and traveling vortex sheets for 2D incompressible Euler equation,
which are supported on several small closed curves. These examples represent a new type …

We prove a bifurcation result of uniformly-rotating/stationary non-trivial vortex sheets near
the circular distribution for a model of two irrotational fluids with same density taking into …

Fluid dynamics is a research area lying at the crossroads of physics and applied
mathematics with an ever-expanding range of applications in natural sciences and …

We construct a new type of planar Euler flows with localized vorticity. Let,, be m arbitrarily
fixed constants. For any given nondegenerate critical point of the Kirchhoff–Routh function …