57 citations · 89 across the 13 of their papers we have counts for
19 papers
Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation
Luigi De Rosa, Mickaël Latocca, Jaemin Park
For any initial datum it is proved the existence of a global-in-time weak solution to the surface quasi-geostrophic equat…
Dissipation concentration in two-dimensional fluids
Luigi De Rosa, Jaemin Park
We study the dissipation measure arising in the inviscid limit of two-dimensional incompressible fluids. It is proved that the dissipation is Lebesgue in time and, for almost every…
Dissipation for codimension 1 singular structures in the incompressible Euler equations
Luigi De Rosa, Marco Inversi, Matteo Nesi
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…
Normal traces and applications to continuity equations on bounded domains
Gianluca Crippa, Luigi De Rosa, Marco Inversi +1
In this work, we study several properties of the normal Lebesgue trace of vector fields introduced by the second and third author in [22] in the context of the energy conservation…
No anomalous dissipation in two-dimensional incompressible fluids
Luigi De Rosa, Jaemin Park
We prove that any sequence of vanishing viscosity Leray-Hopf solutions to the periodic two-dimensional incompressible Navier-Stokes equations does not display anomalous dissipation…
Dissipation in Onsager's critical classes and energy conservation in with and without boundary
Luigi De Rosa, Marco Inversi
This paper is concerned with the incompressible Euler equations. In Onsager's critical classes we provide explicit formulas for the Duchon-Robert measure in terms of the regulariza…
Full double Hölder regularity of the pressure in bounded domains
Luigi De Rosa, Mickaël Latocca, Giorgio Stefani
We consider Hölder continuous weak solutions , , of the incompressible Euler equations on a bounded and simply connected domain $Ω\subset\mat…
Fine properties of symmetric and positive matrix fields with bounded divergence
Luigi De Rosa, Riccardo Tione
This paper is concerned with various fine properties of the functional \[ \mathbb{D}(A) = \int_{\mathbb{T}^n}{\text{det}}^\frac{1}{n-1}(A(x))\,dx \] introduced in [33]. This functi…
Intermittency and lower dimensional dissipation in incompressible fluids
Luigi De Rosa, Philip Isett
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 fo…
On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains
Luigi De Rosa, Mickaël Latocca, Giorgio Stefani
We prove that the hydrodynamic pressure associated to the velocity , , of an inviscid incompressible fluid in a bounded and simply connected domain $Ω\s…
Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces
Luigi De Rosa, Marco Inversi, Giorgio Stefani
In the class of admissible weak solutions, we prove a weak-strong uniqueness result for the incompressible Euler equations assuming that the symmetric part of the gradient belongs…
Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations
Luigi De Rosa, Silja Haffter
For , we consider weak solutions of the incompressible Euler equations that do not conserve the kinetic energy. We prove that for such so…
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…
Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
Maria Colombo, Luigi De Rosa, Luigi Forcella
Given any solution of the Euler equations which is assumed to have some regularity in space - in terms of Besov norms, natural in this context - we show by interpolation method…
Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations
Luigi De Rosa, Riccardo Tione
This paper is devoted to show a couple of typicality results for weak solutions of the Euler equations, in the case . It is known that convex integration schemes…
On the upper semicontinuity of a quasiconcave functional
Luigi De Rosa, Denis Serre, Riccardo Tione
In the recent paper \cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}…
On a question of D. Serre
Luigi De Rosa, Riccardo Tione
In this paper we give a negative answer to the question posed in [15, Open Question 2.1] about possible gains of integrability of determinants of divergence-free, non-negative defi…
Infinitely many Leray-Hopf solutions for the fractional Navier-Stokes equations
Luigi De Rosa
We prove the ill-posedness for the Leray-Hopf weak solutions of the incompressible and ipodissipative Navier-Stokes equations, when the power of the diffusive term is $γ<…
Ill-posedness of Leray solutions for the ipodissipative Navier-Stokes equations
Maria Colombo, Camillo De Lellis, Luigi De Rosa
We prove the ill-posedness of Leray solutions to the Cauchy problem for the ipodissipative Navier--Stokes equations, when the dissipative term is a fractional Laplacian wi…