Publications
Research leading to some of the publications listed on this page was supported by the National Science Foundation through grants NSF DMS-2511625 (2025–2028), NSF DMS-2206677 (2022–2026), NSF CAREER DMS-1514761 (2016–2021), DMS-1412748 (2014–2017), DMS-1109682 (2011–2014), DMS-0807636 (2008–2011), by the CNS SPARK grant (2024–2028), and by the Feodor-Lynen Fellowship (2006–2007).
Research Publications
M. Gualdani and W. Sun.
Uniqueness for the Homogeneous Landau-Coulomb Equation in L3/2.
Under Review.
Uniqueness for the Homogeneous Landau-Coulomb Equation in L3/2.
Under Review.
J. Bedrossian, J. Chen, M.P. Gualdani, S. Ji, V. Vicol, and J. Yang.
Finite time singularities in the Landau equation with very hard potentials.
Under Review.
Finite time singularities in the Landau equation with very hard potentials.
Under Review.
M. Gualdani, N. Guillen, N. Pavlovic and M. Taskovic.
The fuzzy Landau equation: global well-posedness and Fisher information.
Under Review
The fuzzy Landau equation: global well-posedness and Fisher information.
Under Review
M. Gualdani, N. Pavlovic, J. Toyota and D. Wynter.
From the quantum Boltzmann operator to the quantum Landau operator. To appear in Journal of Mathematical Physics (2026).
From the quantum Boltzmann operator to the quantum Landau operator. To appear in Journal of Mathematical Physics (2026).
R. Alonso, M. Gualdani and W. Sun.
The M-Operator and uniqueness of nonlinear kinetic equations.
To appear in Pure and Applied Functional Analysis (2026).
The M-Operator and uniqueness of nonlinear kinetic equations.
To appear in Pure and Applied Functional Analysis (2026).
F. Caja, M. Delgadino, M. Gualdani and M. Taskovic.
Contractivity of Wasserstein distance and exponential decay for the Landau equation with Maxwellian molecules.
under Review
Contractivity of Wasserstein distance and exponential decay for the Landau equation with Maxwellian molecules.
under Review
L. Desvillettes, W. Golding, M. Gualdani and A. Loher.
Production of the Fisher information for the Landau-Coulomb equation with L^1 initial data.
Under review.
Production of the Fisher information for the Landau-Coulomb equation with L^1 initial data.
Under review.
M. Gualdani, M. Ispizua and N. Zamponi.
A quasilinear Keller-Segel with saturated discontinuous advection.
Comm. Partial Differential Equations 51 (2026), no. 2-3, 99-130.
A quasilinear Keller-Segel with saturated discontinuous advection.
Comm. Partial Differential Equations 51 (2026), no. 2-3, 99-130.
M. Bonforte, M. Gualdani and P. Ibarrondo.
Time-Fractional Porous Medium Type Equations. Sharp Time Decay and Regularization.
Calc. Var. Partial Differential Equations 65 (2026), no. 1, Paper No. 30, 40 pp.
Time-Fractional Porous Medium Type Equations. Sharp Time Decay and Regularization.
Calc. Var. Partial Differential Equations 65 (2026), no. 1, Paper No. 30, 40 pp.
M. Gualdani, R. Winter.
A blow-down mechanism for the Landau-Coulomb equation.
J. Funct. Anal. 288 (2025), no. 7, Paper No. 110816, 36 pp.
A blow-down mechanism for the Landau-Coulomb equation.
J. Funct. Anal. 288 (2025), no. 7, Paper No. 110816, 36 pp.
W. Golding, M. Gualdani and A. Loher.
Global smooth solutions to the Landau-Coulomb equation in L^{3/2}.
Arch. Ration. Mech. Anal. 249 (2025), no. 3, Paper No. 34.
Global smooth solutions to the Landau-Coulomb equation in L^{3/2}.
Arch. Ration. Mech. Anal. 249 (2025), no. 3, Paper No. 34.
R. Cabrera, M. Gualdani and N. Guillen.
Regularization estimates of the Landau-Coulomb diffusion.
Nonlinear Anal. 251 (2025), Paper No. 113695, 8 pp.
Regularization estimates of the Landau-Coulomb diffusion.
Nonlinear Anal. 251 (2025), Paper No. 113695, 8 pp.
W. Golding, M. Gualdani and A. Loher.
Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium.
SIAM J. Math. Anal. 56 (2024), no. 6, 8037-8069.
Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium.
SIAM J. Math. Anal. 56 (2024), no. 6, 8037-8069.
W. Golding, M.P. Gualdani and N. Zamponi.
Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential.
Commun. Math. Sci. 20 (2022), no. 8, 2315-2365.
Existence of smooth solutions to the Landau-Fermi-Dirac equation with Coulomb potential.
Commun. Math. Sci. 20 (2022), no. 8, 2315-2365.
M.P. Gualdani and N. Guillen.
Hardy's inequality and the isotropic Landau equation.
J. Funct. Anal. 283 (2022), no. 6, Paper No. 109559.
Hardy's inequality and the isotropic Landau equation.
J. Funct. Anal. 283 (2022), no. 6, Paper No. 109559.
J. Bedrossian, M. Gualdani, S. Snelson.
Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations.
Trans. Amer. Math. Soc. 375 (2022), no. 3, 2187- 2216. https://arxiv.org/pdf/2105.03942.pdf.
Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations.
Trans. Amer. Math. Soc. 375 (2022), no. 3, 2187- 2216. https://arxiv.org/pdf/2105.03942.pdf.
E. Daus, M. Gualdani, J. Xu, N. Zamponi and X. Zhang.
Nonlocal porous media equations with fractional time derivative.
Nonlinear Anal. 211 (2021), Paper No. 112486, 35 pp. https://arxiv.org/pdf/2010.16332.pdf.
Nonlocal porous media equations with fractional time derivative.
Nonlinear Anal. 211 (2021), Paper No. 112486, 35 pp. https://arxiv.org/pdf/2010.16332.pdf.
F. Golse, M. Gualdani, C. Imbert and A. Vasseur.
Partial regularity in time for the space homogeneous Landau equation with Coulomb potential.
Ann. Sci. Ec. Norm. Super. (4) 55 (2022), no. 6, 1575-1611. https://arxiv.org/pdf/1906.02841.pdf.
Partial regularity in time for the space homogeneous Landau equation with Coulomb potential.
Ann. Sci. Ec. Norm. Super. (4) 55 (2022), no. 6, 1575-1611. https://arxiv.org/pdf/1906.02841.pdf.
J.L. Chern and M. Gualdani.
Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions.
Math. Res. Lett. 29 (2022), no. 4, 945-960. https://arxiv.org/pdf/1910.06216.pdf.
Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions.
Math. Res. Lett. 29 (2022), no. 4, 945-960. https://arxiv.org/pdf/1910.06216.pdf.
L. Caffarelli, M. Gualdani and N. Zamponi.
A nonlocal porous media equation.
Comm. Partial Differential Equations 45 (2020), no. 12, 1799-1819.
A nonlocal porous media equation.
Comm. Partial Differential Equations 45 (2020), no. 12, 1799-1819.
E. Daus, M. Gualdani and N. Zamponi.
Long time behavior and weak-strong uniqueness for a nonlocal porous media equation.
J. Differential Equations 268 (2020), no. 4, 1820-1839.
Long time behavior and weak-strong uniqueness for a nonlocal porous media equation.
J. Differential Equations 268 (2020), no. 4, 1820-1839.
M.P. Gualdani and N. Guillen.
On Ap weights and the Landau equations.
Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:17
On Ap weights and the Landau equations.
Calc. Var. Partial Differential Equations 58 (2019), no. 1, 58:17
M.P. Gualdani and N. Zamponi.
Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential.
SIAM J. Math. Anal. 50 (2018), no. 4, 3676 -3714.
Global existence of weak even solutions for an isotropic Landau equation with Coulomb potential.
SIAM J. Math. Anal. 50 (2018), no. 4, 3676 -3714.
M.P. Gualdani and N. Zamponi.
A Review on an isotropic Landau model.
PDE models for multi-agent phenomena, 115-144, Springer INdAM Ser., 28, Springer, Cham, 2018.
A Review on an isotropic Landau model.
PDE models for multi-agent phenomena, 115-144, Springer INdAM Ser., 28, Springer, Cham, 2018.
M.P. Gualdani and N. Zamponi.
Spectral gap and exponential convergence to equilibrium for a multi-species Landau system.
Bull. Sci. Math. 141 (2017), no. 6, 509 - 538.
Spectral gap and exponential convergence to equilibrium for a multi-species Landau system.
Bull. Sci. Math. 141 (2017), no. 6, 509 - 538.
M.P.Gualdani, S. Mischler and C. Mouhot.
Factorization for non-symmetric operators and exponential H-theorem.
Memoires de la SMF 153 (2017), 137 pages.
Factorization for non-symmetric operators and exponential H-theorem.
Memoires de la SMF 153 (2017), 137 pages.
M.P. Gualdani and N. Guillen.
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential.
http://arxiv.org/pdf/1412.0146.pdf. Analysis & PDE, Vol. 9 (2016), No. 8, 1772 - 1809.
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential.
http://arxiv.org/pdf/1412.0146.pdf. Analysis & PDE, Vol. 9 (2016), No. 8, 1772 - 1809.
M.d.M Gonzalez, M.P. Gualdani and J.Sola-Morales.
Instability and bifurcation in a trend depending price formation model.
http://arxiv.org/pdf/1306.1116.pdf. Acta Appl. Math. 144 (2016), 121-136.
Instability and bifurcation in a trend depending price formation model.
http://arxiv.org/pdf/1306.1116.pdf. Acta Appl. Math. 144 (2016), 121-136.
M.P. Gualdani, M.d.M Gonzalez and H. Shahgholian.
A discrete Bernoulli free boundary problem.
Proceedings of the St. Petersburg Mathematical Society, Volume XV:
Advances in Mathematical Analysis of Partial Differential Equations, (2014) 119-140.
A discrete Bernoulli free boundary problem.
Proceedings of the St. Petersburg Mathematical Society, Volume XV:
Advances in Mathematical Analysis of Partial Differential Equations, (2014) 119-140.
J. A. Carrillo, M.d.M Gonzalez, M.P.Gualdani and M.E. Schonbek.
Classical Solutions for a nonlinear Fokker-Planck equation arising in Computational Neuroscience.
Comm. Partial Differential Equations 38 (2013), no. 3, 385 - 409.
Classical Solutions for a nonlinear Fokker-Planck equation arising in Computational Neuroscience.
Comm. Partial Differential Equations 38 (2013), no. 3, 385 - 409.
A. Arnold, I.M.Gamba, M.P.Gualdani, S. Mischler, C. Mouhot and C. Sparber.
The Wigner-Fokker-Planck equation: Stationary states and large time behavior.
Math. Models Methods Appl. Sci. 22 (2012), no. 11, 1250034 -1250065.
The Wigner-Fokker-Planck equation: Stationary states and large time behavior.
Math. Models Methods Appl. Sci. 22 (2012), no. 11, 1250034 -1250065.
M.d.M Gonzalez, M.P. Gualdani.
Some non-standard Sobolev spaces: interpolation and its application to PDE.
Acta Appl. Math. 121 (2012), 57-67.
Some non-standard Sobolev spaces: interpolation and its application to PDE.
Acta Appl. Math. 121 (2012), 57-67.
M.d.M Gonzalez, M.P. Gualdani.
Asymptotics for a free-boundary problem in price formation.
Nonlinear Analysis 74 (2011), pp. 3269-3294.
Asymptotics for a free-boundary problem in price formation.
Nonlinear Analysis 74 (2011), pp. 3269-3294.
L. Chayes, M.d.M Gonzalez, M.P. Gualdani and I. Kim.
Global existence and uniqueness of solutions to a model in price formation.
SIAM J. Math. Anal. Volume 41, Issue 5, pp. 2107-2135 (2009).
Global existence and uniqueness of solutions to a model in price formation.
SIAM J. Math. Anal. Volume 41, Issue 5, pp. 2107-2135 (2009).
I.M. Gamba, M.P. Gualdani, C. Sparber.
A note on the time-decay of solutions for the linearized Wigner-Poisson system.
Kinetic and Related Models, Volume: 2, Number: 1, March 2009.
A note on the time-decay of solutions for the linearized Wigner-Poisson system.
Kinetic and Related Models, Volume: 2, Number: 1, March 2009.
I.M. Gamba, M. P. Gualdani and P. Zhang.
On the blowing up of solutions to a quantum hydrodynamic model on a bounded domain.
Monats. Math. 157 (2009), no. 1, 37-54.
On the blowing up of solutions to a quantum hydrodynamic model on a bounded domain.
Monats. Math. 157 (2009), no. 1, 37-54.
I.M. Gamba, M.P. Gualdani and R. Sharp.
An Adaptable Discontinuous Galerkin Scheme for the Wigner-Fokker-Planck Equation.
Comm. Math. Sci. (2009) Vol. 7, No.3, 635-664.
An Adaptable Discontinuous Galerkin Scheme for the Wigner-Fokker-Planck Equation.
Comm. Math. Sci. (2009) Vol. 7, No.3, 635-664.
M.d.M Gonzalez, M.P. Gualdani.
Asymptotics for a symmetric equation in price formation.
Applied Mathematics and Optimization: Volume 59, Issue 2 (2009), Page 233-246.
Asymptotics for a symmetric equation in price formation.
Applied Mathematics and Optimization: Volume 59, Issue 2 (2009), Page 233-246.
J. A. Carrillo, M. P. Gualdani, and A. Jüngel.
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in R^d.
Publ. Mat. 52 (2008), 413-433.
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in R^d.
Publ. Mat. 52 (2008), 413-433.
J. A. Carrillo, M. Di Francesco, M. P. Gualdani.
Semidiscretization and long-time asymptotics of nonlinear diffusion equations.
Comm. Math. Sci. Supplemental Issue, No.1, 21-53 (2007).
Semidiscretization and long-time asymptotics of nonlinear diffusion equations.
Comm. Math. Sci. Supplemental Issue, No.1, 21-53 (2007).
M. P. Gualdani, A. Jüngel, G. Toscani.
A nonlinear fourth-order parabolic equation with non-homogeneous boundary conditions.
SIAM J. Math. Anal. 37 (2006), No. 6, 1761-1779.
A nonlinear fourth-order parabolic equation with non-homogeneous boundary conditions.
SIAM J. Math. Anal. 37 (2006), No. 6, 1761-1779.
J. A. Carrillo, M. P. Gualdani, G. Toscani.
Finite speed of propagation in porous media by mass transportation methods.
C. R. Acad. Sci. Paris, Ser. I 338 (2004) 815-818.
Finite speed of propagation in porous media by mass transportation methods.
C. R. Acad. Sci. Paris, Ser. I 338 (2004) 815-818.
M. P. Gualdani, A. Jüngel.
Analysis of the viscous quantum hydrodynamic equations for semiconductors.
Europ. J. Appl. Math., (2004) vol. 15, 577-595.
Analysis of the viscous quantum hydrodynamic equations for semiconductors.
Europ. J. Appl. Math., (2004) vol. 15, 577-595.
M. P. Gualdani, A. Jüngel, and G. Toscani.
Exponential decay in time of solutions of the viscous quantum hydrodynamic equations.
Appl. Math. Lett. 16 (2003), 1273-1278.
Exponential decay in time of solutions of the viscous quantum hydrodynamic equations.
Appl. Math. Lett. 16 (2003), 1273-1278.
M. P. Gualdani.
On a Mathematical model for the crystallization of Polymers.
Bollettino U.M.I. (8) 6-B (2003), 161-179.
On a Mathematical model for the crystallization of Polymers.
Bollettino U.M.I. (8) 6-B (2003), 161-179.