A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …

In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …

Some classical and recent results on the Euler equations governing perfect (incompressible
and inviscid) fluid motion are collected and reviewed, with some small novelties scattered …

It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D
incompressible Euler equation is locally well-posed in the class of velocity fields with Hölder …

Inspired by the numerical evidence of a potential 3D Euler singularity\cite
{luo2014potentially, luo2013potentially-2}, we prove finite time blowup of the 2D Boussinesq …

Preface “... ad alcuno, dico, di quelli, che troppo laconicamente vorrebbero vedere, nei piu
angusti spazii che possibil fusse, ristretti i filosofici insegnamenti, sı che sempre si usasse …

We prove nonlinear asymptotic stability of a large class of monotonic shear flows among
solutions of the 2D Euler equations in the channel $\mathbb {T}\times [0, 1] $. More …

Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou 30, 31
and the recent breakthrough by Elgindi 11 on the singularity formation of the 3D Euler …

We prove asymptotic stability of the Couette flow for the 2D Euler equations in the domain T
* 0, 1 T× 0, 1. More precisely we prove that if we start with a small and smooth perturbation …

It is well known that the incompressible Euler equations in two dimensions have globally
regular solutions. The inviscid surface quasi-geostrophic (SQG) equation has a Biot-Savart …