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Regularity estimates in transport equations via heat flow and quantitative differentiation
Elia Brué, Maria Colombo, Guido De Philippis +1
The paper establishes quantitative estimates for commutators in transport equations, showing how logarithmic Sobolev regularity propagates via heat flow and using quantitative diff…
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-Stoke…
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 arbitrar…
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…
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}_{\…
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…