Fluid Flows and Irregular Transport

Pointwise Convergence of the Schrödinger Flow

Autori: Erin Compaan, Renato Lucà, Gigliola Staffilani
Pubblicato in: International Mathematics Research Notices, 2020, ISSN 1073-7928
Editore: Oxford University Press
DOI: 10.1093/imrn/rnaa036

The rectifiability of the entropy defect measure for Burgers equation

Autori: Elio Marconi
Pubblicato in: Journal of Functional Analysis, Numero 283, 2022, ISSN 0022-1236
Editore: Academic Press
DOI: 10.1016/j.jfa.2022.109568

Growth of Sobolev norms and loss of regularity in transport equations

Autori: Gianluca Crippa; Tarek Elgindi; Gautam Iyer; Anna L. Mazzucato
Pubblicato in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Numero 380, 2022, ISSN 1364-503X
Editore: Royal Society of London
DOI: 10.1098/rsta.2021.0024

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

Autori: Giuseppe Genovese, Renato Lucà
Pubblicato in: Mathematical Physics, Analysis and Geometry, Numero 22/3, 2019, ISSN 1385-0172
Editore: 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

Autori: Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Pubblicato in: Calculus of Variations and Partial Differential Equations, Numero 59/1, 2020, ISSN 0944-2669
Editore: Springer Verlag
DOI: 10.1007/s00526-019-1659-0

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

Autori: Stefano Bianchini, Paolo Bonicatto
Pubblicato in: Discrete & Continuous Dynamical Systems - A, Numero 0/0, 2019, Pagina/e 0-0, ISSN 1553-5231
Editore: AIMS
DOI: 10.3934/dcds.2020384

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

Autori: Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Pubblicato in: Journal of Nonlinear Science, Numero 30/6, 2020, Pagina/e 2787-2820, ISSN 0938-8974
Editore: Springer Verlag
DOI: 10.1007/s00332-020-09635-8

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

Autori: Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
Pubblicato in: journal de mathématiques pures et appliquées, 2022, ISSN 0021-7824
Editore: Elsevier BV
DOI: 10.48550/arxiv.2107.03659

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

Autori: Stefano Bianchini, Paolo Bonicatto
Pubblicato in: Inventiones mathematicae, Numero 220/1, 2020, Pagina/e 255-393, ISSN 0020-9910
Editore: 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

Autori: Paolo Bonicatto, Nikolay Gusev
Pubblicato in: Rendiconti Lincei - Matematica e Applicazioni, Numero 30/3, 2019, Pagina/e 511-531, ISSN 1120-6330
Editore: Accademia Nazionale dei Lincei
DOI: 10.4171/rlm/858

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

Autori: Laura Caravenna, Gianluca Crippa
Pubblicato in: Comptes Rendus Mathematique, Numero 354/12, 2016, Pagina/e 1168-1173, ISSN 1631-073X
Editore: Elsevier Masson
DOI: 10.1016/j.crma.2016.10.009

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

Autori: Gianluca Crippa, Silvia Ligabue, Chiara Saffirio
Pubblicato in: Kinetic & Related Models, Numero 11/6, 2018, Pagina/e 1277-1299, ISSN 1937-5077
Editore: AIMS
DOI: 10.3934/krm.2018050

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

Autori: Gianluca Crippa, Camilla Nobili, Christian Seis, Stefano Spirito
Pubblicato in: SIAM Journal on Mathematical Analysis, Numero 49/5, 2017, Pagina/e 3973-3998, ISSN 0036-1410
Editore: Society for Industrial and Applied Mathematics
DOI: 10.1137/17m1130988

A note on pointwise convergence for the Schrödinger equation

Autori: RENATO LUCÀ, KEITH M. ROGERS
Pubblicato in: Mathematical Proceedings of the Cambridge Philosophical Society, 2017, Pagina/e 1-10, ISSN 0305-0041
Editore: Cambridge University Press
DOI: 10.1017/S0305004117000743

Optimality of integrability estimates for advection–diffusion equations

Autori: Stefano Bianchini, Maria Colombo, Gianluca Crippa, Laura V. Spinolo
Pubblicato in: Nonlinear Differential Equations and Applications NoDEA, Numero 24/4, 2017, ISSN 1021-9722
Editore: Birkhauser Verlag
DOI: 10.1007/s00030-017-0455-9

Cellular mixing with bounded palenstrophy

Autori: Gianluca Crippa, Christian Schulze
Pubblicato in: Mathematical Models and Methods in Applied Sciences, Numero 27/12, 2017, Pagina/e 2297-2320, ISSN 0218-2025
Editore: World Scientific Publishing Co
DOI: 10.1142/s0218202517500452

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

Autori: Piero D’Ancona, Renato Lucà
Pubblicato in: Journal of Mathematical Fluid Mechanics, Numero 20/2, 2018, Pagina/e 819-852, ISSN 1422-6928
Editore: Birkhauser Verlag
DOI: 10.1007/s00021-017-0349-y

A limiting absorption principle for the Helmholtz equation with variable coefficients

Autori: Federico Cacciafesta, Piero D'Ancona, Renato Lucà
Pubblicato in: Journal of Spectral Theory, Numero 8/4, 2018, Pagina/e 1349-1392, ISSN 1664-039X
Editore: EMS Publishing House
DOI: 10.4171/jst/229

Invariant measures for the periodic derivative nonlinear Schrödinger equation

Autori: Giuseppe Genovese, Renato Lucà, Daniele Valeri
Pubblicato in: Mathematische Annalen, 2018, ISSN 0025-5831
Editore: Springer Verlag
DOI: 10.1007/s00208-018-1754-0

Exponential self-similar mixing by incompressible flows

Autori: Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Pubblicato in: Journal of the American Mathematical Society, 2018, Pagina/e 1, ISSN 0894-0347
Editore: American Mathematical Society
DOI: 10.1090/jams/913

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

Autori: Giovanni Alberti, Gianluca Crippa, Anna L. Mazzucato
Pubblicato in: Annals of PDE, Numero 5/1, 2019, ISSN 2524-5317
Editore: Springer
DOI: 10.1007/s40818-019-0066-3

On the Singular Local Limit for Conservation Laws with Nonlocal Fluxes

Autori: Maria Colombo, Gianluca Crippa, Laura V. Spinolo
Pubblicato in: Archive for Rational Mechanics and Analysis, Numero 233/3, 2019, Pagina/e 1131-1167, ISSN 0003-9527
Editore: Springer Verlag
DOI: 10.1007/s00205-019-01375-8

Polynomial mixing under a certain stationary Euler flow

Autori: Gianluca Crippa, Renato Lucà, Christian Schulze
Pubblicato in: Physica D: Nonlinear Phenomena, Numero 394, 2019, Pagina/e 44-55, ISSN 0167-2789
Editore: Elsevier BV
DOI: 10.1016/j.physd.2019.01.009

Existence Results for Minimizers of Parametric Elliptic Functionals

Autori: Guido De Philippis, Antonio De Rosa, Francesco Ghiraldin
Pubblicato in: The Journal of Geometric Analysis, 2019, ISSN 1050-6926
Editore: 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

Autori: Caravenna, Laura; Crippa, Gianluca
Pubblicato in: Communications in Partial Differential Equations, 2021, ISSN 0360-5302
Editore: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1883650

Optimal Besov Differentiability for Entropy Solutions of the Eikonal Equation

Autori: Francesco Ghiraldin, Xavier Lamy
Pubblicato in: Communications on Pure and Applied Mathematics, Numero 73/2, 2019, Pagina/e 317-349, ISSN 0010-3640
Editore: 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

Autori: Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura V.
Pubblicato in: ESAIM Math. Model. Numer. Anal., 2021, ISSN 2822-7840
Editore: EDP Sciences
DOI: 10.1051/m2an/2021073

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

Autori: Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
Pubblicato in: Archive for Rational Mechanics and Analysis, 2021, ISSN 0003-9527
Editore: Springer Verlag
DOI: 10.1007/s00205-021-01612-z

Indecomposable sets of finite perimeter in doubling metric measure spaces

Autori: Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
Pubblicato in: Calculus of Variations and Partial Differential Equations, Numero 59/2, 2020, ISSN 0944-2669
Editore: Springer Verlag
DOI: 10.1007/s00526-020-1725-7

Sub-exponential mixing of generalized cellular flows with bounded palenstrophy

Autori: Gianluca Crippa, Christian Schulze
Pubblicato in: Mathematics in Engineering, 2022, ISSN 2640-3501
Editore: AIMS Press
DOI: 10.3934/mine.2023006

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

Autori: Elio Marconi
Pubblicato in: Calculus of Variations and Partial Differential Equations, Numero 61, 2022, ISSN 0944-2669
Editore: Springer Verlag
DOI: 10.1007/s00526-021-02137-9

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

Autori: Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Pubblicato in: Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 2021, ISSN 0294-1449
Editore: 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

Autori: Paolo Bonicatto, Elio Marconi
Pubblicato in: Communications in Partial Differential Equations, Numero 46, 2021, ISSN 0360-5302
Editore: Marcel Dekker Inc.
DOI: 10.1080/03605302.2021.1931883

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

Autori: Giorgio Stefani
Pubblicato in: 2020
Editore: NN

On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains

Autori: Luigi De Rosa, Mickaël Latocca, Giorgio Stefani
Pubblicato in: 2022
Editore: NN
DOI: 10.48550/arxiv.2205.00929

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

Autori: Maria Colombo, Gianluca Crippa, Elio Marconi, Laura V. Spinolo
Pubblicato in: 2022
Editore: NN
DOI: 10.48550/arxiv.2206.03949

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

Autori: Gianluca Crippa, Giorgio Stefani
Pubblicato in: 2021
Editore: NN
DOI: 10.48550/arxiv.2110.15648

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

Autori: Luigi De Rosa, Marco Inversi, Giorgio Stefani
Pubblicato in: 2022
Editore: NN
DOI: 10.48550/arxiv.2204.12779

Structure and regularity of solutions to 1d scalar conservation laws

Autori: Elio Marconi
Pubblicato in: 2019
Editore: NN

Recent results on the singular local limit for nonlocal conservation laws

Autori: Colombo, Maria; Crippa, Gianluca; Graff, Marie; Spinolo, Laura Valentina
Pubblicato in: 2019
Editore: NN

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

Autori: Maria Colombo, Gianluca Crippa, Massimo Sorella
Pubblicato in: 2022
Editore: NN
DOI: 10.48550/arxiv.2207.06833

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

Autori: Paolo Bonicatto, Nikolay A. Gusev
Pubblicato in: Advances in Calculus of Variations, 2021
Editore: NN

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

Autori: Elia Bruè, Mattia Calzi, Giovanni E. Comi, Giorgio Stefani
Pubblicato in: 2020
Editore: NN

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

Autori: Paolo Bonicatto, Stefano Bianchini
Pubblicato in: 2020
Editore: AIMS

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

Autori: Ciampa, Gennaro; Crippa, Gianluca; Spirito, Stefano
Pubblicato in: Hyperbolic Problems: Theory, Numerics, Applications, 2020
Editore: AIMS

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