8 papers
Anomalous dissipation via spontaneous stochasticity with a two-dimensional autonomous velocity field
Carl Johan Peter Johansson, Massimo Sorella
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in (with arbitrary…
Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines
Michele Dolce, Carl Johan Peter Johansson, Massimo Sorella
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 = \nabla…
Nontrivial absolutely continuous part of anomalous dissipation measures in time
Carl Johan Peter Johansson, Massimo Sorella
We positively answer Question 2.2 and Question 2.3 in [Bruè, De Lellis, 2023] in dimension by building new examples of solutions to the forced incompressible Navier-Stokes…
Onsager critical solutions of the forced Navier-Stokes equations
Elia Bruè, Maria Colombo, Gianluca Crippa +2
We answer positively to [BDL22, Question 2.4] by building new examples of solutions to the forced 3d-Navier-Stokes equations with vanishing viscosity, which exhibit anomalous dissi…
Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence
Maria Colombo, Gianluca Crippa, Massimo Sorella
The Obukhov-Corrsin theory of scalar turbulence [Obu49, Cor51] advances quantitative predictions on passive-scalar advection in a turbulent regime and can be regarded as the analog…
Non-uniqueness of integral curves for autonomous Hamiltonian vector fields
Vikram Giri, Massimo Sorella
In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r< d-1and d>=4 for which the associated transport equation has non-unique pos…
The four-state problem and convex integration for linear differential operators
Massimo Sorella, Riccardo Tione
We show that the four-state problem for general linear differential operators is flexible. The only flexibility result available in this context is the one for the five-state probl…
Typicality results for weak solutions of the incompressible Navier--Stokes equations
Maria Colombo, Luigi De Rosa, Massimo Sorella
In this work we show that, in the class of distributional solutions of the incompressible Navier-Stokes system, the ones which are smooth in som…