58 citations · 261 across the 47 of their papers we have counts for
6 papers · 1 filter
An overview on the local limit of non-local conservation laws, and a new proof of a compactness estimate
Maria Colombo, Gianluca Crippa, Elio Marconi +1
Consider a non-local (i.e., involving a convolution term) conservation law: when the convolution term converges to a Dirac delta, in the limit we formally recover a classical (or "…
A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a un…
Mixing in incompressible flows: transport, dissipation, and their interplay
Michele Coti Zelati, Gianluca Crippa, Gautam Iyer +1
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mi…
Weak and parabolic solutions of advection-diffusion equations with rough velocity field
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
We study the Cauchy problem for the advection-diffusion equation associated with a merely integrable divergence-free vector field defi…
Strong convergence of the vorticity and conservation of the energy for the -Euler equations
Stefano Abbate, Gianluca Crippa, Stefano Spirito
In this paper, we study the convergence of solutions of the -Euler equations to solutions of the Euler equations on the -dimensional torus. In particular, given an initial vo…
Ole\uınik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit
Giuseppe Maria Coclite, Maria Colombo, Gianluca Crippa +5
We consider a class of nonlocal conservation laws with exponential kernel and prove that quantities involving the nonlocal term $W:=\mathbb{1}_{(-\infty,0]}(\cdot)\exp(\cdot) \ast…