57 citations · 413 across the 51 of their papers we have counts for
6 papers · 1 filter
Estimate on the dimension of the singular set of the supercritical surface quasigeostrophic equation
Maria Colombo, Silja Haffter
We consider the SQG equation with dissipation given by a fractional Laplacian of order . We introduce a notion of suitable weak solution, which exists for every $L^2…
On the commutativity of flows of rough vector fields
Maria Colombo, Riccardo Tione
In the class of Sobolev vector fields in of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the…
Mixing and diffusion for rough shear flows
Maria Colombo, Michele Coti Zelati, Klaus Widmayer
This article addresses mixing and diffusion properties of passive scalars advected by rough () shear flows. We show that in general, one cannot expect a rough shear flow to in…
On the logarithmic epiperimetric inequality for the obstacle problem
Luca Spolaor, Bozhidar Velichkov
We give three different proofs of the log-epiperimetric inequality at singular points for the obstacle problem. In the first, direct proof, we write the competitor explicitly; the…
Stability of optimal traffic plans in the irrigation problem
Maria Colombo, Antonio de Rosa, Andrea Marchese +2
We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This is the Lagrangian cou…
Positive solutions of transport equations and classical nonuniqueness of characteristic curves
Elia Bruè, Maria Colombo, Camillo De Lellis
The seminal work of DiPerna and Lions [Invent. Math., 98, 1989] guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suita…