We construct infinitely many admissible weak solutions to the 2D incompressible Euler
equations for vortex sheet initial data. Our initial datum has vorticity concentrated on a …

For any 2< p<∞ we prove that there exists an initial velocity field v∘∈ L 2 with vorticity ω∘∈
L 1∩ L p for which there are infinitely many bounded admissible solutions v∈ C t L 2 to the …

In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for
individual turbulent flow realisations modelled by incompressible Navier–Stokes equations …

In this paper, we prove the first existence result of weak solutions to the 3D Euler equation
with initial vorticity concentrated in a circle and velocity field in $ C ([0, T], L^{2^-}) $. The …

We investigate maximal potential energy dissipation as a selection criterion for subsolutions
(coarse grained solutions) in the setting of the unstable Muskat problem. We show that both …

This paper presents a numerical study of a pair of water drops simultaneously and non-
simultaneously impacting on a heated surface using smoothed particle hydrodynamics …

We review recent mathematical results on the theory of ideal MHD turbulence. On the one
hand, we explain a mathematical version of Taylor's conjecture on magnetic helicity …

We provide a quick proof of the existence of mixing weak solutions for the Muskat problem
with variable mixing speed. Our proof is considerably shorter and extends previous results in …

We construct mixing solutions to the incompressible porous media equation starting from
Muskat type data in the partially unstable regime. In particular, we consider bubble and …

We study several different aspects of the energy equipartition principle for water waves. We
prove a virial identity that implies that the potential energy is equal, on average, to a …