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Fluid Flows and Irregular Transport

Total Cost €


EC-Contrib. €






Project "FLIRT" data sheet

The following table provides information about the project.


Organization address
address: PETERSPLATZ 1
city: BASEL
postcode: 4051

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Switzerland [CH]
 Project website
 Total cost 1˙009˙351 €
 EC max contribution 1˙009˙351 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2015-STG
 Funding Scheme ERC-STG
 Starting year 2016
 Duration (year-month-day) from 2016-06-01   to  2021-05-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT BASEL CH (BASEL) coordinator 1˙009˙351.00


 Project objective

'Several important partial differential equations (PDEs) arising in the mathematical description of physical phenomena exhibit transport features: physical quantities are advected by velocity fields that drive the dynamics of the system. This is the case for instance for the Euler equation of fluid dynamics, for conservation laws, and for kinetic equations. An ubiquitous feature of these phenomena is their intrinsic lack of regularity. From the mathematical point of view this stems from the nonlinearity and/or nonlocality of the PDEs. Moreover, the lack of regularity also encodes actual properties of the underlying physical systems: conservation laws develop shocks (discontinuities that propagate in time), solutions to the Euler equation exhibit rough and 'disordered' behaviors. This irregularity is the major difficulty in the mathematical analysis of such problems, since it prevents the use of many standard methods, foremost the classical (and powerful) theory of characteristics. For these reasons, the study in a non smooth setting of transport and continuity equations, and of flows of ordinary differential equations, is a fundamental tool to approach challenging important questions concerning these PDEs. This project aims at establishing: (1) deep insight into the structure of solutions of nonlinear PDEs, in particular the Euler equation and multidimensional systems of conservation laws, (2) rigorous bounds for mixing phenomena in fluid flows, phenomena for which giving a precise mathematical formulation is extremely challenging. The unifying factor of this proposal is that the analysis will rely on major advances in the theory of flows of ordinary differential equations in a non smooth setting, thus providing a robust formulation via characteristics for the PDEs under consideration. The guiding thread is the crucial role of geometric measure theory techniques, which are extremely efficient to describe and investigate irregular phenomena.'


year authors and title journal last update
List of publications.
2019 Maria Colombo, Gianluca Crippa, Laura V. Spinolo
On the Singular Local Limit for Conservation Laws with Nonlocal Fluxes
published pages: 1131-1167, ISSN: 0003-9527, DOI: 10.1007/s00205-019-01375-8
Archive for Rational Mechanics and Analysis 233/3 2019-08-30
2018 Paolo Bonicatto, Nikolay A. Gusev
Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
published pages: , ISSN: , DOI:
2019 Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Loss of Regularity for the Continuity Equation with Non-Lipschitz Velocity Field
published pages: , ISSN: 2524-5317, DOI: 10.1007/s40818-019-0066-3
Annals of PDE 5/1 2019-08-30
2017 Stefano Bianchini, Paolo Bonicatto
A uniqueness result for the decomposition of vector fields in Rd
published pages: , ISSN: , DOI:
2019 Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
On smooth approximations of rough vector fields and the selection of flows
published pages: , ISSN: , DOI:
2019 Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura Valentina
Recent results on the singular local limit for nonlocal conservation laws
published pages: , ISSN: , DOI:
2018 Colombo, Maria; Crippa, Gianluca; Spinolo, Laura V.
Blow-up of the total variation in the local limit of a nonlocal traffic model
published pages: , ISSN: , DOI:
2019 Elio Marconi
Structure and regularity of solutions to 1d scalar conservation laws
published pages: , ISSN: , DOI:
2018 Caravenna, Laura; Crippa, Gianluca
A Directional Lipschitz Extension Lemma, with Applications to Uniqueness and Lagrangianity for the Continuity Equation
published pages: , ISSN: , DOI:
2019 Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
Existence Results for Minimizers of Parametric Elliptic Functionals
published pages: , ISSN: 1050-6926, DOI: 10.1007/s12220-019-00165-8
The Journal of Geometric Analysis 2019-08-30
2019 Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
Smooth approximation is not a selection principle for the transport equation with rough vector field
published pages: , ISSN: , DOI:
2019 Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy
published pages: , ISSN: , DOI:
2019 Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura V.
On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws
published pages: , ISSN: , DOI:
2019 Gianluca Crippa, Renato Lucà, Christian Schulze
Polynomial mixing under a certain stationary Euler flow
published pages: 44-55, ISSN: 0167-2789, DOI: 10.1016/j.physd.2019.01.009
Physica D: Nonlinear Phenomena 394 2019-08-30
2019 Stefano Bianchini, Paolo Bonicatto
Untangling of trajectories for non-smooth vector fields and Bressan\'s Compactness Conjecture
published pages: , ISSN: , DOI:
2018 Francesco Ghiraldin, Xavier Lamy
Optimal Besov differentiability for entropy solutions of the Eikonal equation
published pages: , ISSN: , DOI:
2017 Gianluca Crippa, Camilla Nobili, Christian Seis, Stefano Spirito
Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with $L^1$ Vorticity
published pages: 3973-3998, ISSN: 0036-1410, DOI: 10.1137/17m1130988
SIAM Journal on Mathematical Analysis 49/5 2019-07-08
2017 Stefano Bianchini, Maria Colombo, Gianluca Crippa, Laura V. Spinolo
Optimality of integrability estimates for advection–diffusion equations
published pages: , ISSN: 1021-9722, DOI: 10.1007/s00030-017-0455-9
Nonlinear Differential Equations and Applications NoDEA 24/4 2019-07-08
2018 Giuseppe Genovese, Renato Lucà, Daniele Valeri
Invariant measures for the periodic derivative nonlinear Schrödinger equation
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-018-1754-0
Mathematische Annalen 2019-07-08
2018 Gianluca Crippa, Silvia Ligabue, Chiara Saffirio
Lagrangian solutions to the Vlasov-Poisson system with a point charge
published pages: 1277-1299, ISSN: 1937-5077, DOI: 10.3934/krm.2018050
Kinetic & Related Models 11/6 2019-07-08
2017 Gianluca Crippa, Christian Schulze
Cellular mixing with bounded palenstrophy
published pages: 2297-2320, ISSN: 0218-2025, DOI: 10.1142/s0218202517500452
Mathematical Models and Methods in Applied Sciences 27/12 2019-07-08
2018 Federico Cacciafesta, Piero D\'Ancona, Renato Lucà
A limiting absorption principle for the Helmholtz equation with variable coefficients
published pages: 1349-1392, ISSN: 1664-039X, DOI: 10.4171/jst/229
Journal of Spectral Theory 8/4 2019-07-08
2016 Laura Caravenna, Gianluca Crippa
Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation
published pages: 1168-1173, ISSN: 1631-073X, DOI: 10.1016/j.crma.2016.10.009
Comptes Rendus Mathematique 354/12 2019-07-08
2018 Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Exponential self-similar mixing by incompressible flows
published pages: 1, ISSN: 0894-0347, DOI: 10.1090/jams/913
Journal of the American Mathematical Society 2019-04-10
2018 Piero D’Ancona, Renato Lucà
Stability Properties of the Regular Set for the Navier–Stokes Equation
published pages: 819-852, ISSN: 1422-6928, DOI: 10.1007/s00021-017-0349-y
Journal of Mathematical Fluid Mechanics 20/2 2019-04-10

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