Fluid Flows and Irregular Transport

Publications

Peer reviewed articles (33)

Pointwise Convergence of the Schrödinger Flow

Author(s): Erin Compaan, Renato Lucà, Gigliola Staffilani
Published in: International Mathematics Research Notices, 2020, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnaa036

The rectifiability of the entropy defect measure for Burgers equation

Author(s): Elio Marconi
Published in: Journal of Functional Analysis, 283, 2022, ISSN 0022-1236
Publisher: Academic Press
DOI: 10.1016/j.jfa.2022.109568

Growth of Sobolev norms and loss of regularity in transport equations

Author(s): Gianluca Crippa; Tarek Elgindi; Gautam Iyer; Anna L. Mazzucato
Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380, 2022, ISSN 1364-503X
Publisher: Royal Society of London
DOI: 10.1098/rsta.2021.0024

Local Central Limit Theorem for a Random Walk Perturbed in One Point

Author(s): Giuseppe Genovese, Renato Lucà
Published in: Mathematical Physics, Analysis and Geometry, 22/3, 2019, ISSN 1385-0172
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11040-019-9316-6

Smooth approximation is not a selection principle for the transport equation with rough vector field

Author(s): Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Published in: Calculus of Variations and Partial Differential Equations, 59/1, 2020, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-019-1659-0

Forward untangling and applications to the uniqueness problem for the continuity equation

Author(s): Stefano Bianchini, Paolo Bonicatto
Published in: Discrete & Continuous Dynamical Systems - A, 0/0, 2019, Page(s) 0-0, ISSN 1553-5231
Publisher: AIMS
DOI: 10.3934/dcds.2020384

Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy

Author(s): Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Published in: Journal of Nonlinear Science, 30/6, 2020, Page(s) 2787-2820, ISSN 0938-8974
Publisher: Springer Verlag
DOI: 10.1007/s00332-020-09635-8

On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity

Author(s): Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
Published in: journal de mathématiques pures et appliquées, 2022, ISSN 0021-7824
Publisher: Elsevier BV
DOI: 10.48550/arxiv.2107.03659

A uniqueness result for the decomposition of vector fields in $$\mathbb {R}^{{d}}$$

Author(s): Stefano Bianchini, Paolo Bonicatto
Published in: Inventiones mathematicae, 220/1, 2020, Page(s) 255-393, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-019-00928-8

Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

Author(s): Paolo Bonicatto, Nikolay Gusev
Published in: Rendiconti Lincei - Matematica e Applicazioni, 30/3, 2019, Page(s) 511-531, ISSN 1120-6330
Publisher: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/858

Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation

Author(s): Laura Caravenna, Gianluca Crippa
Published in: Comptes Rendus Mathematique, 354/12, 2016, Page(s) 1168-1173, ISSN 1631-073X
Publisher: Elsevier Masson
DOI: 10.1016/j.crma.2016.10.009

Lagrangian solutions to the Vlasov-Poisson system with a point charge

Author(s): Gianluca Crippa, Silvia Ligabue, Chiara Saffirio
Published in: Kinetic & Related Models, 11/6, 2018, Page(s) 1277-1299, ISSN 1937-5077
Publisher: AIMS
DOI: 10.3934/krm.2018050

Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with $L^1$ Vorticity

Author(s): Gianluca Crippa, Camilla Nobili, Christian Seis, Stefano Spirito
Published in: SIAM Journal on Mathematical Analysis, 49/5, 2017, Page(s) 3973-3998, ISSN 0036-1410
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m1130988

A note on pointwise convergence for the Schrödinger equation

Author(s): RENATO LUCÀ, KEITH M. ROGERS
Published in: Mathematical Proceedings of the Cambridge Philosophical Society, 2017, Page(s) 1-10, ISSN 0305-0041
Publisher: Cambridge University Press
DOI: 10.1017/S0305004117000743

Optimality of integrability estimates for advection–diffusion equations

Author(s): Stefano Bianchini, Maria Colombo, Gianluca Crippa, Laura V. Spinolo
Published in: Nonlinear Differential Equations and Applications NoDEA, 24/4, 2017, ISSN 1021-9722
Publisher: Birkhauser Verlag
DOI: 10.1007/s00030-017-0455-9

Cellular mixing with bounded palenstrophy

Author(s): Gianluca Crippa, Christian Schulze
Published in: Mathematical Models and Methods in Applied Sciences, 27/12, 2017, Page(s) 2297-2320, ISSN 0218-2025
Publisher: World Scientific Publishing Co
DOI: 10.1142/s0218202517500452

Stability Properties of the Regular Set for the Navier–Stokes Equation

Author(s): Piero D’Ancona, Renato Lucà
Published in: Journal of Mathematical Fluid Mechanics, 20/2, 2018, Page(s) 819-852, ISSN 1422-6928
Publisher: Birkhauser Verlag
DOI: 10.1007/s00021-017-0349-y

A limiting absorption principle for the Helmholtz equation with variable coefficients

Author(s): Federico Cacciafesta, Piero D'Ancona, Renato Lucà
Published in: Journal of Spectral Theory, 8/4, 2018, Page(s) 1349-1392, ISSN 1664-039X
Publisher: EMS Publishing House
DOI: 10.4171/jst/229

Invariant measures for the periodic derivative nonlinear Schrödinger equation

Author(s): Giuseppe Genovese, Renato Lucà, Daniele Valeri
Published in: Mathematische Annalen, 2018, ISSN 0025-5831
Publisher: Springer Verlag
DOI: 10.1007/s00208-018-1754-0

Exponential self-similar mixing by incompressible flows

Author(s): Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Published in: Journal of the American Mathematical Society, 2018, Page(s) 1, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/913

Loss of Regularity for the Continuity Equation with Non-Lipschitz Velocity Field

Author(s): Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Published in: Annals of PDE, 5/1, 2019, ISSN 2524-5317
Publisher: Springer
DOI: 10.1007/s40818-019-0066-3

On the Singular Local Limit for Conservation Laws with Nonlocal Fluxes

Author(s): Maria Colombo, Gianluca Crippa, Laura V. Spinolo
Published in: Archive for Rational Mechanics and Analysis, 233/3, 2019, Page(s) 1131-1167, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-019-01375-8

Polynomial mixing under a certain stationary Euler flow

Author(s): Gianluca Crippa, Renato Lucà, Christian Schulze
Published in: Physica D: Nonlinear Phenomena, 394, 2019, Page(s) 44-55, ISSN 0167-2789
Publisher: Elsevier BV
DOI: 10.1016/j.physd.2019.01.009

Existence Results for Minimizers of Parametric Elliptic Functionals

Author(s): Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
Published in: The Journal of Geometric Analysis, 2019, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-019-00165-8

A Directional Lipschitz Extension Lemma, with Applications to Uniqueness and Lagrangianity for the Continuity Equation

Author(s): Caravenna, Laura; Crippa, Gianluca
Published in: Communications in Partial Differential Equations, 2021, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1883650

Optimal Besov Differentiability for Entropy Solutions of the Eikonal Equation

Author(s): Francesco Ghiraldin, Xavier Lamy
Published in: Communications on Pure and Applied Mathematics, 73/2, 2019, Page(s) 317-349, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21868

On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws

Author(s): Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura V.
Published in: ESAIM Math. Model. Numer. Anal., 2021, ISSN 2822-7840
Publisher: EDP Sciences
DOI: 10.1051/m2an/2021073

Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit

Author(s): Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Published in: Archive for Rational Mechanics and Analysis, 2021, ISSN 0003-9527
Publisher: Springer Verlag
DOI: 10.1007/s00205-021-01612-z

Indecomposable sets of finite perimeter in doubling metric measure spaces

Author(s): Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
Published in: Calculus of Variations and Partial Differential Equations, 59/2, 2020, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-020-1725-7

Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

Author(s): Gianluca Crippa, Christian Schulze
Published in: Mathematics in Engineering, 2022, ISSN 2640-3501
Publisher: AIMS Press
DOI: 10.3934/mine.2023006

On the structure of weak solutions to scalar conservation laws with finite entropy production

Author(s): Elio Marconi
Published in: Calculus of Variations and Partial Differential Equations, 61, 2022, ISSN 0944-2669
Publisher: Springer Verlag
DOI: 10.1007/s00526-021-02137-9

Local limit of nonlocal traffic models: convergence results and total variation blow-up

Author(s): Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Published in: Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 2021, ISSN 0294-1449
Publisher: Elsevier BV
DOI: 10.1016/j.anihpc.2020.12.002

Regularity estimates for the flow of BV autonomous divergence free vector fields in R^2

Author(s): Paolo Bonicatto, Elio Marconi
Published in: Communications in Partial Differential Equations, 46, 2021, ISSN 0360-5302
Publisher: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1931883

Other (16)

Generalized Bakry-Émery curvature condition and equivalent entropic inequalities in groups

Author(s): Giorgio Stefani
Published in: 2020
Publisher: NN

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Author(s): Luigi De Rosa, Mickaël Latocca, Giorgio Stefani
Published in: 2022
Publisher: NN
DOI: 10.48550/arxiv.2205.00929

Nonlocal traffic models with general kernels: singular limit, entropy admissibility, and convergence rate

Author(s): Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Published in: 2022
Publisher: NN
DOI: 10.48550/arxiv.2206.03949

An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces

Author(s): Gianluca Crippa, Giorgio Stefani
Published in: 2021
Publisher: NN
DOI: 10.48550/arxiv.2110.15648

Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces

Author(s): Luigi De Rosa, Marco Inversi, Giorgio Stefani
Published in: 2022
Publisher: NN
DOI: 10.48550/arxiv.2204.12779

A uniqueness result for the decomposition of vector fields in Rd

Author(s): Stefano Bianchini, Paolo Bonicatto
Published in: 2017
Publisher: NN

Smooth approximation is not a selection principle for the transport equation with rough vector field

Author(s): Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
Published in: 2019
Publisher: NN

Untangling of trajectories for non-smooth vector fields and Bressan's Compactness Conjecture

Author(s): Stefano Bianchini, Paolo Bonicatto
Published in: 2019
Publisher: NN

Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow

Author(s): Paolo Bonicatto, Nikolay A. Gusev
Published in: 2018
Publisher: NN

Blow-up of the total variation in the local limit of a nonlocal traffic model

Author(s): Colombo, Maria; Crippa, Gianluca; Spinolo, Laura V.
Published in: 2018
Publisher: NN

Structure and regularity of solutions to 1d scalar conservation laws

Author(s): Elio Marconi
Published in: 2019
Publisher: NN

Recent results on the singular local limit for nonlocal conservation laws

Author(s): Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura Valentina
Published in: 2019
Publisher: NN

Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy

Author(s): Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Published in: 2019
Publisher: NN

Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence

Author(s): Maria Colombo, Gianluca Crippa, Massimo Sorella
Published in: 2022
Publisher: NN
DOI: 10.48550/arxiv.2207.06833

On the structure of divergence-free measures on R^2

Author(s): Paolo Bonicatto, Nikolay A. Gusev
Published in: Advances in Calculus of Variations, 2021
Publisher: NN

A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics II

Author(s): Elia Bruè, Mattia Calzi, Giovanni E. Comi, Giorgio Stefani
Published in: 2020
Publisher: NN

Conference proceedings (2)

Untangling of trajectories for non-smooth vector fields and Bressan's compactness conjecture

Author(s): Paolo Bonicatto, Stefano Bianchini
Published in: 2020
Publisher: AIMS

On smooth approximations of rough vector fields and the selection of flows

Author(s): Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
Published in: Hyperbolic Problems: Theory, Numerics, Applications, 2020
Publisher: AIMS