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Time-periodic non-radial solutions near monotone vortices in linearized 2D Euler
Ángel Castro, Daniel Lear
We study the linearized 2D Euler equations around radial vortex profiles. Previous works have shown that the strict monotonicity of the vorticity profile leads to axisymmetrization…
Traveling waves near Poiseuille flow for the 2D Euler equation
Ángel Castro, Daniel Lear
In this paper we reveal the existence of a large family of new, nontrivial and Lipschitz traveling waves for the 2D Euler equation at an arbitrarily small distance from the Poiseui…
Time periodic solutions for the 2D Euler equation near Taylor-Couette flow
Ángel Castro, Daniel Lear
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…
Singularity formation for the fractional Euler-Alignment system in 1D
Victor Arnaiz, Ángel Castro
We study the formation of singularities for the Euler-Alignment system with influence function in 1D. As in [20] the problem is reduced to the analysis of a n…