In this paper, we establish the existence of time quasi-periodic solutions to generalized
surface quasi-geostrophic equation $({\rm gSQG}) _\alpha $ in the patch form close to …

We construct time quasi-periodic vortex patch solutions with one hole for the planar Euler
equations. These structures are captured close to any annulus provided that its modulus …

In this paper, we shall implement KAM theory in order to construct a large class of time quasi-
periodic solutions for an active scalar model arising in fluid dynamics. More precisely, the …

We prove the existence of small amplitude time quasi‐periodic solutions of the pure gravity
water waves equations with constant vorticity, for a bidimensional fluid over a flat bottom …

In this paper, we highlight the importance of the boundary effects on the construction of
quasi-periodic vortex patches solutions close to Rankine vortices and whose existence is …

We prove the existence of time-quasi-periodic solutions of the incompressible Euler
equation on the three-dimensional torus T 3, with a small time-quasi-periodic external force …

We prove the existence of time quasi-periodic vortex patch solutions of the 2 d-Euler
equations in R 2, close to uniformly rotating Kirchhoff elliptical vortices, with aspect ratios …

In the present contribution, we first prove the existence of $\mathbf {m} $-fold simply-
connected V-states close to the unit disc for Euler-$\alpha $ equations. These solutions are …

We prove the existence of small amplitude time quasi-periodic vortex patch solutions of the
2D-Euler equations close to Kirchhoff elliptical vortices. These solutions exist for all ellipse …

We develop KAM theory close to an elliptic fixed point for quasi-linear Hamiltonian
perturbations of the dispersive Degasperis–Procesi equation on the circle. The overall …