6 citations · 6 across the 7 of their papers we have counts for
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Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The purpose of this note is twofold. First, we prove quantitative estimates for the Ambrosio-Trevisan commutator which implies propagation of logarithmic Sobolev regularity. Second…
Lyapunov exponents, entropy and mixing for DiPerna-Lions flows
Elia Brué, Maria Colombo, Carl Johan Peter Johansson
The main goal of this work is to establish an asymptotic form of Bressan's mixing conjecture. To this end, we develop an ergodic-theoretic framework for incompressible DiPerna-Lion…
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…
Wild solutions to scalar Euler-Lagrange equations
Carl Johan Peter Johansson
We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether solutions are necessarily $W^{1,2}_{\…
configurations and hyperbolic systems
Carl Johan Peter Johansson, Riccardo Tione
In this paper we study the rank-one convex hull of a differential inclusion associated to entropy solutions of a hyperbolic system of conservation laws. This was introduced in Sect…