G. Bae, M. Pirner, S. Warnecke, Numerical schemes for a multi-species quantum BGK model, submitted, 2023
M. Pirner, G. Toshpulatov, Hypocoercivity for the non-linear semiconductor Boltzmann equation, submitted, 2024
M. Pirner, A consistent kinetic Fokker-Planck model for gas mixtures, Journal of Statistical Physics, 191, 143 (2024)
T. Herzing, C. Klingenberg, M. Pirner, Hypocoercivity of the linearized BGK equation with stochastic coefficients, Methods and Applications of Analysis 30(3),113-128 (2023)
G. Favre, M. Pirner, C. Schmeiser, Hypocoercivity and reaction-diffusion limit for a non-linear generation-recombination model, Archive for Rational Mechanics and Analysis 247, 72 (2023)
G. Bae, C. Klingenberg, M. Pirner, S.-B. Yun, BGK model for multi-component gases near a global Maxwellian, SIAM Journal of Mathematical Analysis 55 (2), 2023
J. Haack, C. Hauck, C. Klingenberg, M. Pirner, S. Warnecke, Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency, Journal of Computational Physics 473: 111729 (2022)
G. Favre, M. Pirner, C. Schmeiser, Thermalization of a rarefied gas with total energy conservation: existence, hypocoercivity, macroscopic limit, Kinetic and Related Models, 15 (5): 823-841 (2022)
M. Pirner, A review on BGK models for gas mixtures of mono and polyatomic molecules, Fluids 6, 11, 393 (2021)
J. Haack, C. Hauck, C. Klingenberg, M. Pirner, S. Warnecke, A consistent BGK model with velocity-dependent collision frequency for gas mixtures, Journal of Statistical Physics 184, 31 (2021)
G. Bae, C. Klingenberg, M. Pirner, S. Yun, BGK model of the multi-species Uehling Uhlenbeck equation, Kinetic & Related Models (2021) 14 (1): 25-44
A. Crestetto, C. Klingenberg, M. Pirner, Kinetic/fluid micro-macro numerical scheme for a two component gas mixture, SIAM Multiscale Modeling and Simulation 18.2, pp. 970-998 (2020)
L. Liu, M. Pirner, Hypocoercivity for a BGK model for gas mixtures, Journal of Differential Equations 267 (2019) 119-149
C. Klingenberg, M. Pirner, G. Puppo, A consistent kinetic model for a two-component mixture of polyatomic molecules, Communications in Mathematical Sciences, Vol. 17, No. 1 (2019), pp. 149-173
M. Pirner, A BGK model for gas mixtures of polyatomic molecules allowing for slow and fast relaxation of the temperatures, Journal of Statistical Physics, 173(6), 1660-1687 (2018)
C. Klingenberg, M. Pirner, Existence, Uniqueness and Positivity of solutions for BGK models for mixtures, Journal of Differential Equations 264, pp. 207-227 (2018)
C Klingenberg, M. Pirner, G. Puppo, A consistent kinetic model for a two component mixture with an application to plasma, Kinetic and Related Models Vol. 10, No. 2, pp. 445-465 (2017)
L. Baumann, M. Pirner, Linear Landau damping for a two-species Vlasov-Poisson system for electrons and ions, accepted for publication in the proceedings of the XVIII International Conference on Hyperbolic Problems (HYP 2022), 2023
M. Pirner, S. Warnecke, A review on a general multi-species BGK model: modeling, theory and numerics, From Kinetic Theory to Turbulence Modeling: The Legacy of Carlo Cercignani, Springer Nature (2023)
M. Pirner, On multi-species BGK models with velocity dependent collision frequencies, Oberwolfach Reports. No. 19/2021 (2021)
Q. Li, C. Klingenberg, M. Pirner, On quantifying uncertainties for the linearized BGK kinetic equation, Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018)
C. Klingenberg, M. Pirner, G. Puppo, Kinetic ES-BGK models for a multi-component gas mixture, Theory, Numerics and Applications of Hyperbolic Problems, Springer Proceedings in Mathematics & Statistics (PROMS) 236 (2018)
PhD thesis (under the supervision of Christian Klingenberg):
M. Pirner, On kinetic modeling of gas mixtures, 2018