Publications

Ciampa, G., Crippa, G. and Spirito, S. (2020) “Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy”, Journal of Nonlinear Science. Springer, 30(6), pp. 2787–2820. doi: 10.1007/s00332-020-09635-8.   edoc
Ciampa, G., Crippa, G. and Spirito, S. (2020) “Smooth approximation is not a selection principle for the transport equations with rough vector field”, Calculus of Variations and Partial Differential Equations . Springer, 59, p. 13. doi: 10.1007/s00526-019-1659-0.   edoc | Open Access
Crippa, G. and Ligabue, S. (2020) “A Note on the Lagrangian Flow Associated to a Partially Regular Vector Field”, Differential Equations and Dynamical Systems. Springer, p. 20 pages. doi: 10.1007/s12591-020-00530-y.   
Colombo, M., Crippa, G., Marconi, E. and Spinolo, L. V. (2020) “Local limit of nonlocal traffic models: Convergence results and total variation blow-up”, Annales de l’Institut Henri Poincaré C, Analyse non linéaire. Elsevier, p. 14. doi: 10.1016/j.anihpc.2020.12.002.   
Ciampa, G., Crippa, G. and Spirito, S. (2019) “Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy”. Universität Basel (Preprints Fachbereich Mathematik , 2019).   edoc | Open Access
Ciampa, G., Crippa, G. and Spirito, S. (2019) “Smooth approximation is not a selection principle for the transport equation with rough vector field”. Universität Basel (Preprints Fachbereich Mathematik, 2019).   edoc | Open Access
Colombo, M., Crippa, G., Graff, M. and Spinolo, L. V. (2019) “On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws”. Universität Basel (Preprints Fachbereich Mathematik, 2019).   edoc | Open Access
Colombo, M., Crippa, G., Graff, M. and Spinolo, L. V. (2019) “Recent results on the singular local limit for nonlocal conservation laws”. Universität Basel (Preprints Fachbereich Mathematik, 2019).   edoc | Open Access
Ciampa, G., Crippa, G. and Spirito, S. (2019) “On smooth approximations of rough vector fields and the selection of flows”. Universität Basel (Preprints Fachbereich Mathematik, 2019).   edoc | Open Access
Alberti, G., Crippa, G. and Mazzucato, A. L. (2019) “Loss of regularity for the continuity equation with non-Lipschitz velocity field”, Annals of PDE. Springer, 5(1), p. 9. doi: 10.1007/s40818-019-0066-3.   edoc | Open Access
Colombo, M., Crippa, G. and Spinolo, L. V. (2019) “On the singular local limit for conservation laws with nonlocal fluxes”, Archive for Rational Mechanics and Analysis. Springer, 233(3), pp. 1131–1167. doi: 10.1007/s00205-019-01375-8.   edoc | Open Access
Crippa, G., Lucà, R. and Schulze, C. (2019) “Polynomial mixing under a certain stationary Euler flow”, Physica D: Nonlinear Phenomena. Elsevier, 394, pp. 44–55. doi: 10.1016/j.physd.2019.01.009.   edoc | Open Access
Alberti, G., Crippa, G. and Mazzucato, A. L. (2019) “Exponential self-similar mixing by incompressible flows”, Journal of the American Mathematical Society. American Mathematical Society (AMS), 32(2), pp. 445–490. doi: 10.1090/jams/913.   edoc | Open Access
Crippa, G., Ligabue, S. and Saffirio, C. (2018) “Lagrangian solutions to the Vlasov-Poissosystem with a point charge”, Kinetic and related models, 11(6), pp. 1277–1299. doi: 10.3934/krm.2018050.   edoc | Open Access
Crippa, G. and Mazzucato, A. (eds.) (2017) Transport, Fluids, and Mixing. Berlin: De Gruyter Open (Partial differential equations and measure theory). Available at: https://www.degruyter.com/view/product/497138.   edoc
Choudhury, A., Crippa, G. and Spinolo, L. V. (2017) “Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system”, Zeitschrift für Angewandte Mathematik und Physik. Springer, 68(138), p. 19. doi: 10.1007/s00033-017-0883-8.   edoc | Open Access
Crippa, G., Nobili, C., Seis, C. and Spirito, S. (2017) “Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L 1 Vorticity ”, SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics, 49(5), pp. 3973–3998. doi: 10.1137/17M1130988.   edoc | Open Access
Crippa, G. and Schulze, C. (2017) “Cellular mixing with bounded palenstrophy”, Mathematical Models and Methods in Applied Sciences. World Scientific Publishing, 27(12), pp. 2297–2320. doi: 10.1142/S0218202517500452.   edoc | Open Access
Bianchini, S., Colombo, M., Crippa, G. and Spinolo, L. V. (2017) “Optimality of integrability estimates for advection-diffusion equations”, Nonlinear Differential Equations and Applications. Elsevier, 24(33), p. 19. doi: 10.1007/s00030-017-0455-9.   edoc | Open Access
Crippa, G., Gusev, N., Spirito, S. and Wiedemann, E. (2017) “Failure of the chain rule for the divergence of bounded vector fields”, Annali della Scuola Normale di Pisa - Classe di Scienze. Scuola Normale Superiore, Pisa, 17(1), pp. 1–18. doi: 10.2422/2036-2145.201506_006.   edoc | Open Access
Crippa, G., Lopes Filho, M., Miot, E. and Nussenzveig Lopes, H. (2016) “Flows of vector fields with point singularities and the vortex-wave system”, Discrete and continuous dynamical systems. American Institute of Mathematical Sciences, 36(5), pp. 2405–2417. doi: 10.3934/dcds.2016.36.2405.   edoc | Open Access
Caravenna, L. and Crippa, G. (2016) “Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation”, Comptes rendus mathematique. Elsevier Masson for Académie de Sciences, 354(12), pp. 1168–1173.   edoc | Open Access
Colombo, M., Crippa, G. and Stefano, S. (2016) “Logarithmic estimates for continuity equations”, Networks and Heterogeneous Media. American Institute of Mathematical Sciences (AIMS) , 11(2), pp. 301–311. doi: 10.3934/nhm.2016.11.301.   edoc | Open Access
Bohun, A., Bouchut, F. and Crippa, G. (2016) “Lagrangian flows for vector fields with anisotropic regularity”, Annales de l’Institut Henri Poincaré (C) Analyse non linéaire. Elsevier, 33(6), pp. 1409–1429. doi: 10.1016/j.anihpc.2015.05.005.   edoc | Open Access
Bohun, A., Bouchut, F. and Crippa, G. (2016) “Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy”, Nonlinear Analysis: Theory, Methods & Applications. Elsevier, 132, pp. 160–172. doi: 10.1016/j.na.2015.11.004.   edoc | Open Access
Bohun, A., Bouchut, F. and Crippa, G. (2016) “Lagrangian solutions to the Vlasov–Poisson system with L1 density”, Journal of differential equations. Elsevier, 260(4), pp. 3576–3597. doi: 10.1016/j.jde.2015.10.041.   edoc | Open Access
Crippa, G., Semenova, E. and Spirito, S. (2015) “Strong continuity for the 2D Euler equations”, Kinetic and related models. American Institute of Mathematical Sciences, 8(4), pp. 685–689. doi: 10.3934/krm.2015.8.685.   edoc | Open Access
Crippa, G. and Spirito, S. (2015) “Renormalized solutions of the 2D Euler equations”, Communications in mathematical physics. Springer, 339(1), pp. 191–198. doi: 10.1007/s00220-015-2411-z.   edoc | Open Access
Colombo, M., Crippa, G. and Spirito, S. (2015) “Renormalized solutions to the continuity equation with an integrable damping term”, Calculus of variations and partial differential equations. Springer, 54(2), pp. 1831–1845. doi: 10.1007/s00526-015-0845-y.   edoc | Open Access
Crippa, G., Gusev, N., Spirito, S. and Wiedemann, E. (2015) “Non-uniqueness and prescribed energy for the continuity equation”, Communications in mathematical sciences. International Press, 13(7), pp. 1937–1947. doi: 10.4310/CMS.2015.v13.n7.a12.   edoc | Open Access
Crippa, G., Donadello, C. and Spinolo, L. V. (2014) “A note on the initial-boundary value problem for continuity equations with rough coefficients”, in Hyperbolic problems: theory, numerics, applications. American Institute of Mathematical Sciences (AIMS on Applied Mathematics, 8), pp. 957–966. Available at: https://aimsciences.org/books/am/AMVol8.html.   edoc | Open Access
Crippa, G. (2014) “Ordinary differential equations and singular integrals”, in Hyperbolic problems: theory, numerics, applications. American Institute of Mathematical Sciences (AIMS on Applied Mathematics, 8), pp. 109–117. Available at: https://aimsciences.org/books/am/AMVol8.html.   edoc | Open Access
Ambrosio, L. and Crippa, G. (2014) “Continuity equations and ODE flows with non-smooth velocity”, Proceedings of the Royal Society of Edinburgh. Section A, Mathematics. The Royal Society, Vol. 144, H. 6, pp. 1191–1244. doi: 10.1017/S0308210513000085.   edoc | Open Access
Crippa, G., Donadello, C. and Spinolo, L. V. (2014) “Initial-boundary value problems for continuity equations with BV coefficients”, Journal de mathématiques pures et appliquées. Gauthier-Villars, Vol. 102, No. 1, pp. 79–98. doi: 10.1016/j.matpur.2013.11.002.   edoc | Open Access
Alberti, G., Crippa, G. and Mazzucato, A. L. (2014) “Exponential self-similar mixing and loss of regularity for continuity equations”, Comptes rendus mathematique. Académie de Sciences, Vol. 352, no. 11, pp. 901–906. doi: 10.1016/j.crma.2014.08.021.   edoc | Open Access
Alberti, G., Bianchini, S. and Crippa, G. (2014) “On the Lp-differentiability of certain classes of functions”, Revista matemática Iberoamericana. EMS, Vol. 30, no. 1, pp. 349–367.   edoc | Open Access
Alberti, G., Bianchini, S. and Crippa, G. (2014) “A uniqueness result for the continuity equation in two dimensions”, Journal of the European Mathematical Society. EMS, Vol. 16, H. 2, pp. 201–234. doi: 10.4171/JEMS/431.   edoc | Open Access
Alberti, G., Bianchini, S. and Crippa, G. (2013) “Structure of level sets and Sard-type properties of Lipschitz maps”, Annali della Scuola Normale di Pisa - Classe di Scienze. Scuola Normale Superiore, Pisa, 12(4), pp. 863–902. doi: 10.2422/2036-2145.201107_006.   edoc | Open Access
Bouchut, F. and Crippa, G. (2013) “Lagrangian flows for vector fields with gradient given by a singular integral”, Journal of hyperbolic differential equations. World Scientific, Vol. 10, H. 2, pp. 235–282. doi: 10.1142/S0219891613500100.   edoc | Open Access
Crippa, G. and Lecureux-Mercier, M. (2013) “Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow”, NoDEA: nonlinear differential equations and applications. Birkhäuser, Vol. 20, H. 3, pp. 523–537. doi: 10.1007/s00030-012-0164-3.   edoc | Open Access
Acerbi, E., Crippa, G. and Mucci, D. (2012) “A variational problem for multifunctions with interaction between leaves”, ESAIM: Control, Optimisation and Calculus of Variations. EDP Sciences, 18(4), pp. 1178–1206. doi: 10.1051/cocv/2011195.   edoc | Open Access
Crippa, G. (2011) “Lagrangian flows and the one-dimensional Peano phenomenon for ODEs”, Journal of Differential Equations. Elsevier, 250(7), pp. 3135–3149. doi: 10.1016/j.jde.2010.12.007.   edoc
Ambrosio, L., Crippa, G., Figalli, A. and Spinolo, L. V. (2009) “Some new well-posedness results for continuity and transport equations, and applications to the chromatography system”, SIAM Journal on Mathematical Analysis. SIAM, 41(5), pp. 1890–1920. doi: 10.1137/090754686.   edoc
Crippa, G., Jimenez, C. and Pratelli, A. (2009) “Optimum and equilibrium in a transport problem with queue penalization effect”, Advances in Calculus of Variations. De Gruyter, 2(3), pp. 207–246. doi: 10.1515/ACV.2009.009.   edoc
Crippa, G. (2009) The flow associated to weakly differentiable vector fields. Pisa: Edizioni della Normale (Theses / Scuola Normale Superiore di Pisa, 12).   edoc
Crippa, G. and De Lellis, C. (2008) “Estimates and regularity results for the DiPerna-Lions flow”, Journal für die reine und angewandte Mathematik. Walter de Gruyter, 2008(616), pp. 15–46. doi: 10.1515/CRELLE.2008.016.   edoc
Ambrosio, L., Crippa, G. and LeFloch, P. G. (2008) “Leaf superposition property for integer rectifiable currents”, Networks and Heterogeneous Media. American Institute of Mathematical Sciences, 3(1), pp. 85–95. doi: 10.3934/nhm.2008.3.85.   edoc
Ambrosio, L. and Crippa, G. (2008) “Existence, uniqueness, stability and differentiability properties of the flow associated to weakly differentiable vector fields”, in Ancona, F., Bianchini, S., Colombo, R. M., De Lellis, C., Marson, A., and Montanari, A. (eds.) Transport equations and multi-D hyperbolic conservation laws. Berlin: Springer, pp. 3–57. doi: 10.1007/978-3-540-76781-7_1.   
Crippa, G., Otto, F. and Westdickenberg, M. (2008) “Regularizing effect of nonlinearity in multidimensional scalar conservation laws”, in Ancona, F., Bianchini, S., Colombo, R. M., De Lellis, C., Marson, A., and Montanari, A. (eds.) Transport equations and multi-D hyperbolic conservation laws. Berlin: Springer, pp. 77–128. doi: 10.1007/978-3-540-76781-7_3.   
Colombini, F., Crippa, G. and Rauch, J. (2006) “A note on two-dimensional transport with bounded divergence”, Communications Partial Differential Equations. Taylor & Francis, 31(7-9), pp. 1109–1115. doi: 10.1080/03605300500455933.   edoc
Bouchut, F. and Crippa, G. (2006) “Uniqueness, renormalization, and smooth approximations for linear transport equations”, SIAM Journal on Mathematical Analysis. SIAM, 38(4), pp. 1316–1328. doi: 10.1137/06065249X.   edoc
Crippa, G. and De Lellis, C. (2006) “Oscillatory solutions to transport equations”, Indiana University Mathematics Journal . Indiana University Mathematics Journal , 55(1), pp. 1–13. doi: 10.1512/iumj.2006.55.2793.   edoc | Open Access
Ambrosio, L., Crippa, G. and Maniglia, S. (2005) “Traces and fine properties of a BD class of vector fields and applications”, Annales de la Faculté des Sciences de Toulouse. Mathématiques. Université Paul Sabatier, 14(4), pp. 527–561. Available at: http://www.numdam.org/item?id=AFST_2005_6_14_4_527_0 .   edoc