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Fluid Flows and Irregular Transport

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Publications

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

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

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


Published in: ISSN 1937-5077
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, Issue 49/5, 2017, Page(s) 3973-3998, ISSN 0036-1410
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
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, Issue 24/4, 2017, ISSN 1021-9722
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, Issue 27/12, 2017, Page(s) 2297-2320, ISSN 0218-2025
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, Issue 20/2, 2018, Page(s) 819-852, ISSN 1422-6928
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, Issue 8/4, 2018, Page(s) 1349-1392, ISSN 1664-039X
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
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
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, Issue 5/1, 2019, ISSN 2524-5317
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, Issue 233/3, 2019, Page(s) 1131-1167, ISSN 0003-9527
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, Issue 394, 2019, Page(s) 44-55, ISSN 0167-2789
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
DOI: 10.1007/s12220-019-00165-8

A uniqueness result for the decomposition of vector fields in Rd

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

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

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

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

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

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

Author(s): Caravenna, Laura; Crippa, Gianluca
Published in: 2018

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

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

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

Structure and regularity of solutions to 1d scalar conservation laws

Author(s): Elio Marconi
Published in: 2019

Optimal Besov differentiability for entropy solutions of the Eikonal equation

Author(s): Francesco Ghiraldin, Xavier Lamy
Published in: 2018

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

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

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: 2019