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 show that suitable transport noises produce anomalous dissipation of
enstrophy and energy of solutions of the 2D Navier-Stokes equations and diffusion …

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 propose a novel approach to induce anomalous dissipation through advection driven by
turbulent fluid flows. Specifically, we establish the existence of a velocity field $ v $ satisfying …

We consider the advection of a passive scalar by a divergence free random Gaussian field,
white in time and H\" older regular in space (rough Kraichnan's model), a well established …

In this paper, we resolve an important long-standing question of Alberti (Rend Lincei 23: 477–
491, 2012) that asks whether or not if there is a continuous vector field with bounded …

Dissipation anomaly, a phenomenon predicted by Kolmogorov's theory of turbulence, is the
persistence of a non-vanishing energy dissipation for solutions of the Navier-Stokes …

We study the evolution of a passive scalar subject to molecular diffusion and advected by an
incompressible velocity field on a 2D bounded domain. The velocity field is u=∇⊥ H, where …

We show that by" accelerating" relaxation enhancing flows, one can construct a flow that is
smooth on $[0, 1)\times\mathbb {T}^ d $ but highly singular at $ t= 1$ so that for any positive …

We study the advection equation along vector fields singular at the initial time. More
precisely, we prove that for divergence-free vector fields in\(L^ 1_ {loc}((0, T]; BV (\mathbb …