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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
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, Nonlinearity, 37. https://doi.org/10.1088/1361-6544/ad1cdf
, & Spirito, Stefano. (2024). Strong convergence of the vorticity and conservation of the energy for the α-Euler equations. Bonicatto, Paolo, Ciampa, Gennaro, & Journal of Evolution Equations, 24. https://doi.org/10.1007/s00028-023-00919-6
. (2024). Weak and parabolic solutions of advection–diffusion equations with rough velocity field. Zelati, Michele Coti, Notices of the American Mathematical Society, 2024-May, 593–604. https://doi.org/10.1090/noti2929
, Iyer, Gautam, & Mazzucato, Anna L. (2024). Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay. Colombo, Maria, Archive for Rational Mechanics and Analysis, 247. https://doi.org/10.1007/s00205-023-01845-0
, Marconi, Elio, & Spinolo, Laura V. (2023). Nonlocal Traffic Models with General Kernels: Singular Limit, Entropy Admissibility, and Convergence Rate. Colombo, Maria, Annals of PDE, 9. https://doi.org/10.1007/s40818-023-00162-9
, & Sorella, Massimo. (2023). Anomalous Dissipation and Lack of Selection in the Obukhov–Corrsin Theory of Scalar Turbulence. Mathematics in Engineering, 5. https://doi.org/10.3934/mine.2023006
, & Schulze, Christian. (2023). Sub-exponential mixing of generalized cellular flows with bounded palenstrophy †. Bonicatto, Paolo, Ciampa, Gennaro, & Journal de Mathématiques Pures et Appliquées, 167, 204–224. https://doi.org/10.1016/j.matpur.2022.09.005
. (2022). On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2225), 20210024. https://doi.org/10.1098/rsta.2021.0024
, Elgindi, Tarek, Iyer, Gautam, & Mazzucato, Anna L. (2022). Growth of Sobolev norms and loss of regularity in transport equations. Caravenna, Laura, & Communications Partial Differential Equations, 46(8), 1488–1520. https://doi.org/10.1080/03605302.2021.1883650
. (2021). A directional Lipschitz extension lemma, with applications to uniqueness and Lagrangianity for the continuity equation. Ciampa, Gennaro, Archive for Rational Mechanics and Analysis, 240(1), 295–326. https://doi.org/10.1007/s00205-021-01612-z
, & Spirito, Stefano. (2021). Strong convergence of the vorticity for the 2D Euler equations in the inviscid limit. Colombo, Maria, ESAIM: Mathematical Modelling and Numerical Analysis, 55(6), 2705–2723. https://doi.org/10.1051/m2an/2021073
, Graff, Marie, & Spinolo, Laura Valentina. (2021). On the role of numerical viscosity in the study of the local limit of nonlocal conservation laws. Colombo, Maria, Annales de l’Institut Henri Poincaré C, Analyse non linéaire, 38(5), 1653–1666. https://doi.org/10.1016/j.anihpc.2020.12.002
, Marconi, Elio, & Spinolo, Laura V. (2021). Local limit of nonlocal traffic models: Convergence results and total variation blow-up. Ciampa, Gennaro, Calculus of Variations and Partial Differential Equations, 59, 13. https://doi.org/10.1007/s00526-019-1659-0
, & Spirito, Stefano. (2020). Smooth approximation is not a selection principle for the transport equations with rough vector field. Ciampa, Gennaro, Journal of Nonlinear Science, 30(6), 2787–2820. https://doi.org/10.1007/s00332-020-09635-8
, & Spirito, Stefano. (2020). Weak Solutions Obtained by the Vortex Method for the 2D Euler Equations are Lagrangian and Conserve the Energy. Differential Equations and Dynamical Systems, 1–20. https://doi.org/10.1007/s12591-020-00530-y
, & Ligabue, Silvia. (2020). A Note on the Lagrangian Flow Associated to a Partially Regular Vector Field. Alberti, Giovanni, Journal of the American Mathematical Society, 32(2), 445–490. https://doi.org/10.1090/jams/913
, & Mazzucato, Anna L. (2019). Exponential self-similar mixing by incompressible flows. Alberti, Giovanni, Annals of PDE, 5(1), 9. https://doi.org/10.1007/s40818-019-0066-3
, & Mazzucato, Anna L. (2019). Loss of regularity for the continuity equation with non-Lipschitz velocity field. Colombo, Maria, Archive for Rational Mechanics and Analysis, 233(3), 1131–1167. https://doi.org/10.1007/s00205-019-01375-8
, & Spinolo, Laura Valentina. (2019). On the singular local limit for conservation laws with nonlocal fluxes. Physica D: Nonlinear Phenomena, 394, 44–55. https://doi.org/10.1016/j.physd.2019.01.009
, Lucà, Renato, & Schulze, Christian. (2019). Polynomial mixing under a certain stationary Euler flow. Kinetic and related models, 11(6), 1277–1299. https://doi.org/10.3934/krm.2018050
, Ligabue, Silvia, & Saffirio, Chiara. (2018). Lagrangian solutions to the Vlasov-Poissosystem with a point charge. Bianchini, Stefano, Colombo, Maria, Nonlinear Differential Equations and Applications, 24(4), 19. https://doi.org/10.1007/s00030-017-0455-9
, & Spinolo, Laura Valentina. (2017). Optimality of integrability estimates for advection-diffusion equations. Choudhury, Anupam, Zeitschrift für Angewandte Mathematik und Physik, 68(6), 19. https://doi.org/10.1007/s00033-017-0883-8
, & Spinolo, Laura Valentina. (2017). Initial-boundary value problems for nearly incompressible vector fields, and applications to the Keyfitz and Kranzer system. Annali della Scuola Normale di Pisa - Classe di Scienze, 17(1), 1–18. https://doi.org/10.2422/2036-2145.201506_006
, Gusev, Nikolay, Spirito, Stefano, & Wiedemann, Emil. (2017). Failure of the chain rule for the divergence of bounded vector fields. Partial differential equations and measure theory. De Gruyter Open. https://www.degruyter.com/view/product/497138
, & Mazzucato, Anna. (2017). Transport, Fluids, and Mixing. In Transport, Fluids, and Mixing: Open Access Partial Differential Equations and Measure Theory, 1–7. https://doi.org/10.1515/9783110571240-001
, & Mazzucato, Anna. (2017). Introduction. Transport, Fluids, and Mixing: Open Access Partial Differential Equations and Measure Theory. https://doi.org/10.1515/9783110571240
, Mazzucato, Anna, Bednarczyk-Drag, Agnieszka, & Leverton, Adam Tod. (2017). SIAM Journal on Mathematical Analysis, 49(5), 3973–3998. https://doi.org/10.1137/17m1130988
, Nobili, Camilla, Seis, Christian, & Spirito, Stefano. (2017). Eulerian and Lagrangian Solutions to the Continuity and Euler Equations with L 1 Vorticity. Mathematical Models and Methods in Applied Sciences, 27(12), 2297–2320. https://doi.org/10.1142/s0218202517500452
, & Schulze, Christian. (2017). Cellular mixing with bounded palenstrophy. Bohun, Anna, Bouchut, Francois, & Annales de l’Institut Henri Poincaré (C) Analyse non linéaire, 33(6), 1409–1429. https://doi.org/10.1016/j.anihpc.2015.05.005
. (2016). Lagrangian flows for vector fields with anisotropic regularity. Bohun, Anna, Bouchut, François, & Journal of differential equations, 260(4), 3576–3597. https://doi.org/10.1016/j.jde.2015.10.041
. (2016). Lagrangian solutions to the Vlasov-Poisson system with L-1 density. Bohun, Anna, Bouchut, François, & Nonlinear Analysis: Theory, Methods & Applications, 132, 160–172. https://doi.org/10.1016/j.na.2015.11.004
. (2016). Lagrangian solutions to the 2D Euler system with L1 vorticity and infinite energy. Caravenna, Laura, & Comptes rendus mathematique, 354(12), 1168–1173. https://doi.org/10.1016/j.crma.2016.10.009
. (2016). Uniqueness and Lagrangianity for solutions with lack of integrability of the continuity equation. Colombo, Maria, Networks and Heterogeneous Media, 11(2), 301–311. https://doi.org/10.3934/nhm.2016.11.301
, & Stefano, Spirito. (2016). Logarithmic estimates for continuity equations. Discrete and continuous dynamical systems, 36(5), 2405–2417. https://doi.org/10.3934/dcds.2016.36.2405
, Lopes Filho, Milton, Miot, Evelyne, & Nussenzveig Lopes, Helena. (2016). Flows of vector fields with point singularities and the vortex-wave system. Colombo, Maria, Calculus of variations and partial differential equations, 54(2), 1831–1845. https://doi.org/10.1007/s00526-015-0845-y
, & Spirito, Stefano. (2015). Renormalized solutions to the continuity equation with an integrable damping term. Communications in mathematical sciences, 13(7), 1937–1947. https://doi.org/10.4310/cms.2015.v13.n7.a12
, Gusev, Nikolay, Spirito, Stefano, & Wiedemann, Emil. (2015). Non-uniqueness and prescribed energy for the continuity equation. Kinetic and related models, 8(4), 685–689. https://doi.org/10.3934/krm.2015.8.685
, Semenova, Elizaveta, & Spirito, Stefano. (2015). Strong continuity for the 2D Euler equations. Communications in mathematical physics, 339(1), 191–198. https://doi.org/10.1007/s00220-015-2411-z
, & Spirito, Stefano. (2015). Renormalized solutions of the 2D Euler equations. Alberti, Giovanni, Bianchini, Stefano, & Journal of the European Mathematical Society, 16(2), 201–234. https://doi.org/10.4171/jems/431
. (2014). A uniqueness result for the continuity equation in two dimensions. Alberti, Giovanni, Bianchini, Stefano, & Revista matemática Iberoamericana, 30(1), 349–367. https://doi.org/10.4171/rmi/782
. (2014). On the Lp-differentiability of certain classes of functions. Alberti, Giovanni, Comptes rendus mathematique, 352(11), 901–906. https://doi.org/10.1016/j.crma.2014.08.021
, & Mazzucato, Anna L. (2014). Exponential self-similar mixing and loss of regularity for continuity equations. Ambrosio, Luigi, & Proceedings of the Royal Society of Edinburgh. Section A, Mathematics, 144(6), 1191–1244. https://doi.org/10.1017/s0308210513000085
. (2014). Continuity equations and ODE flows with non-smooth velocity. AIMS on Applied Mathematics, 8. https://aimsciences.org/books/am/AMVol8.html
. (2014). Ordinary differential equations and singular integrals. Journal de mathématiques pures et appliquées, 102(1), 79–98. https://doi.org/10.1016/j.matpur.2013.11.002
, Donadello, Carlotta, & Spinolo, Laura V. (2014). Initial-boundary value problems for continuity equations with BV coefficients. AIMS on Applied Mathematics, 8. https://aimsciences.org/books/am/AMVol8.html
, Donadello, Carlotta, & Spinolo, Laura Valentina. (2014). A note on the initial-boundary value problem for continuity equations with rough coefficients. Alberti, Giovanni, Bianchini, Stefano, & Annali della Scuola Normale di Pisa - Classe di Scienze, 12(4), 863–902. https://doi.org/10.2422/2036-2145.201107_006
. (2013). Structure of level sets and Sard-type properties of Lipschitz maps. Bouchut, Francois, & Journal of hyperbolic differential equations, 10(2), 235–282. https://doi.org/10.1142/s0219891613500100
. (2013). Lagrangian flows for vector fields with gradient given by a singular integral. NoDEA: nonlinear differential equations and applications, 20(3), 523–537. https://doi.org/10.1007/s00030-012-0164-3
, & Lecureux-Mercier, Magali. (2013). Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. Acerbi, Emilio, ESAIM: Control, Optimisation and Calculus of Variations, 18(4), 1178–1206. https://doi.org/10.1051/cocv/2011195
, & Mucci, Domenico. (2012). A variational problem for multifunctions with interaction between leaves. Journal of Differential Equations, 250(7), 3135–3149. https://doi.org/10.1016/j.jde.2010.12.007
. (2011). Lagrangian flows and the one-dimensional Peano phenomenon for ODEs. Alberti, G., Bianchini, S., & Journal of Mathematical Sciences, 170(3), 283–293. https://doi.org/10.1007/s10958-010-0085-9
(2010). Divergence-free vector fields in ℝ2. 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, SIAM Journal on Mathematical Analysis, 41(5), 1890–1920. https://doi.org/10.1137/090754686
, Figalli, Alessio, & Spinolo, Laura V. (2009). Some new well-posedness results for continuity and transport equations, and applications to the chromatography system. Theses / Scuola Normale Superiore di Pisa (Vol. 12). Edizioni della Normale.
. (2009). The flow associated to weakly differentiable vector fields. In Advances in Calculus of Variations, 2(3), 207–246. https://doi.org/10.1515/acv.2009.009
, Jimenez, Chloé, & Pratelli, Aldo. (2009). Optimum and equilibrium in a transport problem with queue penalization effect. 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, Networks and Heterogeneous Media, 3(1), 85–95. https://doi.org/10.3934/nhm.2008.3.85
, & LeFloch, Philippe G. (2008). Leaf superposition property for integer rectifiable currents. Journal Für Die Reine Und Angewandte Mathematik, 616(616), 15–46. https://doi.org/10.1515/crelle.2008.016
, & De Lellis, Camillo. (2008). Estimates and regularity results for the DiPerna-Lions flow. Ambrosio, Luigi, & Transport equations and multi-D hyperbolic conservation laws (pp. 3–57). Springer. https://doi.org/10.1007/978-3-540-76781-7_1
. (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. 77–128). Springer. https://doi.org/10.1007/978-3-540-76781-7_3
, 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.), Bouchut, François, & SIAM Journal on Mathematical Analysis, 38(4), 1316–1328. https://doi.org/10.1137/06065249x
. (2006). Uniqueness, renormalization, and smooth approximations for linear transport equations. Colombini, Ferruccio, Communications Partial Differential Equations, 31(7), 1109–1115. https://doi.org/10.1080/03605300500455933
, & Rauch, Jeffrey. (2006). A note on two-dimensional transport with bounded divergence. Indiana University Mathematics Journal, 55(1), 1–13. https://doi.org/10.1512/iumj.2006.55.2793
, & De Lellis, Camillo. (2006). Oscillatory solutions to transport equations. Ambrosio, Luigi, Annales de La Faculté Des Sciences de Toulouse. Mathématiques, 14(4), 527–561. https://doi.org/10.5802/afst.1102
, & Maniglia, Stefania. (2005). Traces and fine properties of a BD class of vector fields and applications.