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 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 …

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 address a degenerate elliptic variational problem arising in the application of the least
action principle to averaged solutions of the inhomogeneous Euler equations in the …

We examine the two-dimensional Euler equations including the local energy (in) equality as
a differential inclusion and show that the associated relaxation essentially reduces to the …

We consider the problem of mixing a passive scalar in a periodic box by incompressible
vector fields subject to a fixed energy constraint. In that setting a lower bound for the time in …

The presence of plasma density gradient is one of the main sources of Rayleigh–Taylor
instability (RTI). The Rayleigh–Taylor instability has application in meteorology to explain …