Outputs (4)

A variational approach to first order kinetic Mean Field Games with local couplings (2022)
Journal Article
Griffin-Pickering, M., & Mészáros, A. R. (2022). A variational approach to first order kinetic Mean Field Games with local couplings. Communications in Partial Differential Equations, 47(10), 1945-2022. https://doi.org/10.1080/03605302.2022.2101003

First order kinetic mean field games formally describe the Nash equilibria of deterministic differential games where agents control their acceleration, asymptotically in the limit as the number of agents tends to infinity. The known results for the w... Read More about A variational approach to first order kinetic Mean Field Games with local couplings.

Global strong solutions in R3 for ionic Vlasov-Poisson systems (2021)
Journal Article
Griffin-Pickering, M., & Iacobelli, M. (2021). Global strong solutions in R3 for ionic Vlasov-Poisson systems. Kinetic and Related Models, 14(4), 571-597. https://doi.org/10.3934/krm.2021016

Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-... Read More about Global strong solutions in R3 for ionic Vlasov-Poisson systems.

Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus (2021)
Journal Article
Griffin-Pickering, M., & Iacobelli, M. (2021). Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus. Communications in Partial Differential Equations, 46(10), 1892-1939. https://doi.org/10.1080/03605302.2021.1913750

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonline... Read More about Global well-posedness for the Vlasov-Poisson system with massless electrons in the 3-dimensional torus.

A mean field approach to the quasineutral limit for the Vlasov-Poisson equation (2018)
Journal Article
Griffin-Pickering, M., & Iacobelli, M. (2018). A mean field approach to the quasineutral limit for the Vlasov-Poisson equation. SIAM Journal on Mathematical Analysis, 50(5), 5502-5536. https://doi.org/10.1137/17m1156277

This paper concerns the derivation of the Kinetic Isothermal Euler system in dimension d≥1 from an N-particle system of extended charges with Coulomb interaction. This requires a combined mean field and quasineutral limit for a regularized N-particle... Read More about A mean field approach to the quasineutral limit for the Vlasov-Poisson equation.