Prof. Dr. Gianluca Crippa

Crippa, G., Inversi, M., Saffirio, C., & Stefani, G. (2024). Existence and stability of weak solutions of the Vlasov–Poisson system in localised Yudovich spaces [Journal-article]. Nonlinearity, 37(9), 95015. https://doi.org/10.1088/1361-6544/ad5bb3

Coclite, G. M., Colombo, M., Crippa, G., De Nitti, N., Keimer, A., Marconi, E., Pflug, L., & Spinolo, L. V. (2024). Oleinik-type estimates for nonlocal conservation laws and applications to the nonlocal-to-local limit [Journal-article]. Journal of Hyperbolic Differential Equations, 21(03), 681–705. https://doi.org/10.1142/s021989162440006x

Crippa, G., & Stefani, G. (2024). An elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces [Journal-article]. Calculus of Variations and Partial Differential Equations, 63(7). https://doi.org/10.1007/s00526-024-02750-4

Abbate, Stefano, Crippa, Gianluca, & Spirito, Stefano. (2024). Strong convergence of the vorticity and conservation of the energy for the α-Euler equations. Nonlinearity, 37. https://doi.org/10.1088/1361-6544/ad1cdf

Bonicatto, Paolo, Ciampa, Gennaro, & Crippa, Gianluca. (2024). Weak and parabolic solutions of advection–diffusion equations with rough velocity field. Journal of Evolution Equations, 24. https://doi.org/10.1007/s00028-023-00919-6

Zelati, Michele Coti, Crippa, Gianluca, Iyer, Gautam, & Mazzucato, Anna L. (2024). Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay. Notices of the American Mathematical Society, 2024-May, 593–604. https://doi.org/10.1090/noti2929

Colombo, Maria, Crippa, Gianluca, Marconi, Elio, & Spinolo, Laura V. (2023). Nonlocal Traffic Models with General Kernels: Singular Limit, Entropy Admissibility, and Convergence Rate. Archive for Rational Mechanics and Analysis, 247. https://doi.org/10.1007/s00205-023-01845-0

Colombo, Maria, Crippa, Gianluca, & Sorella, Massimo. (2023). Anomalous Dissipation and Lack of Selection in the Obukhov–Corrsin Theory of Scalar Turbulence. Annals of PDE, 9. https://doi.org/10.1007/s40818-023-00162-9

Crippa, Gianluca, & Schulze, Christian. (2023). Sub-exponential mixing of generalized cellular flows with bounded palenstrophy †. Mathematics in Engineering, 5. https://doi.org/10.3934/mine.2023006

Bonicatto, Paolo, Ciampa, Gennaro, & Crippa, Gianluca. (2022). On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity. Journal de Mathématiques Pures et Appliquées, 167, 204–224. https://doi.org/10.1016/j.matpur.2022.09.005

Crippa, Gianluca, Elgindi, Tarek, Iyer, Gautam, & Mazzucato, Anna L. (2022). Growth of Sobolev norms and loss of regularity in transport equations. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2225), 20210024. https://doi.org/10.1098/rsta.2021.0024

Caravenna, Laura, & Crippa, Gianluca. (2021). A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation. Communications Partial Differential Equations, 46(8), 1488–1520. https://doi.org/10.1080/03605302.2021.1883650

Ciampa, Gennaro, Crippa, Gianluca, & Spirito, Stefano. (2021). Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit. Archive for Rational Mechanics and Analysis, 240(1), 295–326. https://doi.org/10.1007/s00205-021-01612-z

Colombo, Maria, Crippa, Gianluca, Graff, Marie, & Spinolo, Laura Valentina. (2021). On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws. ESAIM: Mathematical Modelling and Numerical Analysis, 55(6), 2705–2723. https://doi.org/10.1051/m2an/2021073

Colombo, Maria, Crippa, Gianluca, Marconi, Elio, & Spinolo, Laura V. (2021). Local limit of nonlocal traffic models: Convergence results and total variation blow-up. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 38(5), 1653–1666. https://doi.org/10.1016/j.anihpc.2020.12.002

Ciampa, Gennaro, Crippa, Gianluca, & Spirito, Stefano. (2020). Smooth approximation is not a selection principle for the transport equations with rough vector field. Calculus of Variations and Partial Differential Equations, 59, 13. https://doi.org/10.1007/s00526-019-1659-0

Ciampa, Gennaro, Crippa, Gianluca, & Spirito, Stefano. (2020). Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy. Journal of Nonlinear Science, 30(6), 2787–2820. https://doi.org/10.1007/s00332-020-09635-8

Crippa, Gianluca, & Ligabue, Silvia. (2020). A Note on the Lagrangian Flow Associated to a Partially Regular Vector Field. Differential Equations and Dynamical Systems, 1–20. https://doi.org/10.1007/s12591-020-00530-y

Alberti, Giovanni, Crippa, Gianluca, & Mazzucato, Anna L. (2019). Exponential self-similar mixing by incompressible flows. Journal of the American Mathematical Society, 32(2), 445–490. https://doi.org/10.1090/jams/913

Alberti, Giovanni, Crippa, Gianluca, & Mazzucato, Anna L. (2019). Loss of regularity for the continuity equation with non-Lipschitz velocity field. Annals of PDE, 5(1), 9. https://doi.org/10.1007/s40818-019-0066-3

Colombo, Maria, Crippa, Gianluca, & Spinolo, Laura Valentina. (2019). On the singular local limit for conservation laws with nonlocal fluxes. Archive for Rational Mechanics and Analysis, 233(3), 1131–1167. https://doi.org/10.1007/s00205-019-01375-8

Crippa, Gianluca, Lucà, Renato, & Schulze, Christian. (2019). Polynomial mixing under a certain stationary Euler flow. Physica D: Nonlinear Phenomena, 394, 44–55. https://doi.org/10.1016/j.physd.2019.01.009

Crippa, Gianluca, Ligabue, Silvia, & Saffirio, Chiara. (2018). Lagrangian solutions to the Vlasov-Poissosystem with a point charge. Kinetic and related models, 11(6), 1277–1299. https://doi.org/10.3934/krm.2018050

Bianchini, Stefano, Colombo, Maria, Crippa, Gianluca, & Spinolo, Laura Valentina. (2017). Optimality of integrability estimates for advection-diffusion equations. Nonlinear Differential Equations and Applications, 24(4), 19. https://doi.org/10.1007/s00030-017-0455-9

Choudhury, Anupam, Crippa, Gianluca, & Spinolo, Laura Valentina. (2017). Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system. Zeitschrift für Angewandte Mathematik und Physik, 68(6), 19. https://doi.org/10.1007/s00033-017-0883-8

Crippa, Gianluca, Gusev, Nikolay, Spirito, Stefano, & Wiedemann, Emil. (2017). Failure of the chain rule for the divergence of bounded vector fields. Annali della Scuola Normale di Pisa - Classe di Scienze, 17(1), 1–18. https://doi.org/10.2422/2036-2145.201506_006

Crippa, Gianluca, & Mazzucato, Anna. (2017). Transport, Fluids, and Mixing. In Partial differential equations and measure theory. De Gruyter Open. https://www.degruyter.com/view/product/497138

Crippa, Gianluca, & Mazzucato, Anna. (2017). Introduction. Transport, Fluids, and Mixing: Open Access Partial Differential Equations and Measure Theory, 1–7. https://doi.org/10.1515/9783110571240-001

Crippa, Gianluca, Mazzucato, Anna, Bednarczyk-Drag, Agnieszka, & Leverton, Adam Tod. (2017). Transport, Fluids, and Mixing: Open Access Partial Differential Equations and Measure Theory. https://doi.org/10.1515/9783110571240

Crippa, Gianluca, Nobili, Camilla, Seis, Christian, & Spirito, Stefano. (2017). Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L 1 Vorticity. SIAM Journal on Mathematical Analysis, 49(5), 3973–3998. https://doi.org/10.1137/17m1130988

Crippa, Gianluca, & Schulze, Christian. (2017). Cellular mixing with bounded palenstrophy. Mathematical Models and Methods in Applied Sciences, 27(12), 2297–2320. https://doi.org/10.1142/s0218202517500452

Bohun, Anna, Bouchut, Francois, & Crippa, Gianluca. (2016). Lagrangian flows for vector fields with anisotropic regularity. Annales de l’Institut Henri Poincaré (C) Analyse non linéaire, 33(6), 1409–1429. https://doi.org/10.1016/j.anihpc.2015.05.005

Bohun, Anna, Bouchut, François, & Crippa, Gianluca. (2016). Lagrangian solutions to the Vlasov-Poisson system with L-1 density. Journal of differential equations, 260(4), 3576–3597. https://doi.org/10.1016/j.jde.2015.10.041

Bohun, Anna, Bouchut, François, & Crippa, Gianluca. (2016). Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy. Nonlinear Analysis: Theory, Methods & Applications, 132, 160–172. https://doi.org/10.1016/j.na.2015.11.004

Caravenna, Laura, & Crippa, Gianluca. (2016). Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation. Comptes rendus mathematique, 354(12), 1168–1173. https://doi.org/10.1016/j.crma.2016.10.009

Colombo, Maria, Crippa, Gianluca, & Stefano, Spirito. (2016). Logarithmic estimates for continuity equations. Networks and Heterogeneous Media, 11(2), 301–311. https://doi.org/10.3934/nhm.2016.11.301

Crippa, Gianluca, Lopes Filho, Milton, Miot, Evelyne, & Nussenzveig Lopes, Helena. (2016). Flows of vector fields with point singularities and the vortex-wave system. Discrete and continuous dynamical systems, 36(5), 2405–2417. https://doi.org/10.3934/dcds.2016.36.2405

Colombo, Maria, Crippa, Gianluca, & Spirito, Stefano. (2015). Renormalized solutions to the continuity equation with an integrable damping term. Calculus of variations and partial differential equations, 54(2), 1831–1845. https://doi.org/10.1007/s00526-015-0845-y

Crippa, Gianluca, Gusev, Nikolay, Spirito, Stefano, & Wiedemann, Emil. (2015). Non-uniqueness and prescribed energy for the continuity equation. Communications in mathematical sciences, 13(7), 1937–1947. https://doi.org/10.4310/cms.2015.v13.n7.a12

Crippa, Gianluca, Semenova, Elizaveta, & Spirito, Stefano. (2015). Strong continuity for the 2D Euler equations. Kinetic and related models, 8(4), 685–689. https://doi.org/10.3934/krm.2015.8.685

Crippa, Gianluca, & Spirito, Stefano. (2015). Renormalized solutions of the 2D Euler equations. Communications in mathematical physics, 339(1), 191–198. https://doi.org/10.1007/s00220-015-2411-z

Alberti, Giovanni, Bianchini, Stefano, & Crippa, Gianluca. (2014). A uniqueness result for the continuity equation in two dimensions. Journal of the European Mathematical Society, 16(2), 201–234. https://doi.org/10.4171/jems/431

Alberti, Giovanni, Bianchini, Stefano, & Crippa, Gianluca. (2014). On the Lp-differentiability of certain classes of functions. Revista matemática Iberoamericana, 30(1), 349–367. https://doi.org/10.4171/rmi/782

Alberti, Giovanni, Crippa, Gianluca, & Mazzucato, Anna L. (2014). Exponential self-similar mixing and loss of regularity for continuity equations. Comptes rendus mathematique, 352(11), 901–906. https://doi.org/10.1016/j.crma.2014.08.021

Ambrosio, Luigi, & Crippa, Gianluca. (2014). Continuity equations and ODE flows with non-smooth velocity. Proceedings of the Royal Society of Edinburgh. Section A, Mathematics, 144(6), 1191–1244. https://doi.org/10.1017/s0308210513000085

Crippa, Gianluca. (2014). Ordinary differential equations and singular integrals. AIMS on Applied Mathematics, 8. https://aimsciences.org/books/am/AMVol8.html

Crippa, Gianluca, Donadello, Carlotta, & Spinolo, Laura V. (2014). Initial-boundary value problems for continuity equations with BV coefficients. Journal de mathématiques pures et appliquées, 102(1), 79–98. https://doi.org/10.1016/j.matpur.2013.11.002

Crippa, Gianluca, Donadello, Carlotta, & Spinolo, Laura Valentina. (2014). A note on the initial-boundary value problem for continuity equations with rough coefficients. AIMS on Applied Mathematics, 8. https://aimsciences.org/books/am/AMVol8.html

Alberti, Giovanni, Bianchini, Stefano, & Crippa, Gianluca. (2013). Structure of level sets and Sard-type properties of Lipschitz maps. Annali della Scuola Normale di Pisa - Classe di Scienze, 12(4), 863–902. https://doi.org/10.2422/2036-2145.201107_006

Bouchut, Francois, & Crippa, Gianluca. (2013). Lagrangian flows for vector fields with gradient given by a singular integral. Journal of hyperbolic differential equations, 10(2), 235–282. https://doi.org/10.1142/s0219891613500100

Crippa, Gianluca, & Lecureux-Mercier, Magali. (2013). Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. NoDEA: nonlinear differential equations and applications, 20(3), 523–537. https://doi.org/10.1007/s00030-012-0164-3

Acerbi, Emilio, Crippa, Gianluca, & Mucci, Domenico. (2012). A variational problem for multifunctions with interaction between leaves. ESAIM: Control, Optimisation and Calculus of Variations, 18(4), 1178–1206. https://doi.org/10.1051/cocv/2011195

Crippa, Gianluca. (2011). Lagrangian flows and the one-dimensional Peano phenomenon for ODEs. Journal of Differential Equations, 250(7), 3135–3149. https://doi.org/10.1016/j.jde.2010.12.007

Alberti, G., Bianchini, S., & Crippa, G. (2010). Divergence-free vector fields in ℝ2. Journal of Mathematical Sciences, 170(3), 283–293. https://doi.org/10.1007/s10958-010-0085-9

Crippa, G., & Spinolo, L. V. (2010). An overview on some results concerning the transport equation and its applications to conservation laws. 9, 1283–1293. https://doi.org/10.3934/cpaa.2010.9.1283

Alberti, G., Bianchini, S., & Crippa, G. (2009). Two-dimensional transport equation with Hamiltonian vector fields (Other) [Other, American Mathematical Society]. 337–346. https://doi.org/10.1090/psapm/067.2/2605229

Ambrosio, Luigi, Crippa, Gianluca, Figalli, Alessio, & Spinolo, Laura V. (2009). Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. SIAM Journal on Mathematical Analysis, 41(5), 1890–1920. https://doi.org/10.1137/090754686

Crippa, Gianluca. (2009). The flow associated to weakly differentiable vector fields. In Theses / Scuola Normale Superiore di Pisa (Vol. 12). Edizioni della Normale.

Crippa, Gianluca, Jimenez, Chloé, & Pratelli, Aldo. (2009). Optimum and equilibrium in a transport problem with queue penalization effect. Advances in Calculus of Variations, 2(3), 207–246. https://doi.org/10.1515/acv.2009.009

Ambrosio, L., Crippa, G., De Lellis, C., Otto, F., & Westdickenberg, M. (2008). Transport Equations and Multi-D Hyperbolic Conservation Laws [Book]. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-76781-7

Ambrosio, Luigi, Crippa, Gianluca, & LeFloch, Philippe G. (2008). Leaf superposition property for integer rectifiable currents. Networks and Heterogeneous Media, 3(1), 85–95. https://doi.org/10.3934/nhm.2008.3.85

Crippa, Gianluca, & De Lellis, Camillo. (2008). Estimates and regularity results for the DiPerna-Lions flow. Journal Für Die Reine Und Angewandte Mathematik, 616(616), 15–46. https://doi.org/10.1515/crelle.2008.016

Ambrosio, Luigi, & Crippa, Gianluca. (2008). Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields. In Ancona, Fabio; Bianchini, Stefano; Colombo, Rinaldo M.; De Lellis, Camillo; Marson, Andrea; Montanari, Annamaria (Ed.), Transport equations and multi-D hyperbolic conservation laws (pp. 3–57). Springer. https://doi.org/10.1007/978-3-540-76781-7_1

Crippa, Gianluca, Otto, Felix, & Westdickenberg, Michael. (2008). Regularizing effect of nonlinearity in multidimensional scalar conservation laws. In Ancona, Fabio; Bianchini, Stefano; Colombo, Rinaldo M.; De Lellis, Camillo; Marson, Andrea; Montanari, Annamaria (Ed.), Transport equations and multi-D hyperbolic conservation laws (pp. 77–128). Springer. https://doi.org/10.1007/978-3-540-76781-7_3

Bouchut, François, & Crippa, Gianluca. (2006). Uniqueness, renormalization, and smooth approximations for linear transport equations. SIAM Journal on Mathematical Analysis, 38(4), 1316–1328. https://doi.org/10.1137/06065249x

Colombini, Ferruccio, Crippa, Gianluca, & Rauch, Jeffrey. (2006). A note on two-dimensional transport with bounded divergence. Communications Partial Differential Equations, 31(7), 1109–1115. https://doi.org/10.1080/03605300500455933

Crippa, Gianluca, & De Lellis, Camillo. (2006). Oscillatory solutions to transport equations. Indiana University Mathematics Journal, 55(1), 1–13. https://doi.org/10.1512/iumj.2006.55.2793

Ambrosio, Luigi, Crippa, Gianluca, & Maniglia, Stefania. (2005). Traces and fine properties of a BD class of vector fields and applications. Annales de La Faculté Des Sciences de Toulouse. Mathématiques, 14(4), 527–561. https://doi.org/10.5802/afst.1102