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 …

Using a new definition for the nonlinear term, we prove that all weak solutions to the SQG
equation (and mSQG) conserve the angular momentum. This result is new for the weak …

We consider the 2D Euler equations on $\R^ 2$ in vorticity form, with unbounded initial
vorticity, perturbed by a suitable non-smooth Kraichnan transport noise, with regularity index …

In this work, we study several properties of the normal Lebesgue trace of vector fields
introduced by the second and third author in [18] in the context of the energy conservation …

We prove that any sequence of vanishing viscosity Leray-Hopf solutions to the periodic two-
dimensional incompressible Navier-Stokes equations does not display anomalous …

In this note, we address the validity of certain exact results from turbulence theory in the
deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 …

We consider weak solutions to the incompressible Euler equations. It is shown that energy
conservation holds in any Onsager critical class in which smooth functions are dense. The …

This paper is concerned with the inhomogeneous incompressible Euler system. We
establish a Duchon--Robert type approximation theorem for the distribution describing the …

In the context of incompressible fluids, the observation that turbulent singular structures fail
to be space filling is known as “intermittency”, and it has strong experimental foundations …

In this paper, we derive the dissipation term in the local energy balance law of weak
solutions for a surface growth model arising in the molecular-beam-epitaxy process by using …