The Vlasov-Maxwell-Boltzmann system near Maxwellians

By Yan Guo. 2003

299 citations recorded by the source corpus.

Subfields: Applied Mathematics, Atomic and Molecular Physics, and Optics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/60628c2bc5d75b07762c79c593063f36a40edf81

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In Applied Mathematics

In Atomic and Molecular Physics, and Optics

In Computational Mechanics

Citations in the corpus

Classical Solutions to the Boltzmann Equation for Molecules with an Angular Cutoff (2003, methodology): “The construction of the global classical solutions is based on an energy method, which was developed recently in the study of the Vlasov-Maxwell(Poisson)-Boltzmann equation [11, 13 ].”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, background): “Later Guo refined his approach in [20] to meet the”
Non-Isothermal Boundary in the Boltzmann Theory and Fourier Law (2013, methodology): “The key macroscopic equations for ξf = (af , bf , cf ) connect Pf and {I −P}f via the Boltzmann equation as in page 621 of [19]: ∆ξf ∼ ∂(2){I−P}f + higher order terms, (1.”
Exponential Decay for Soft Potentials near Maxwellian (2008, methodology): “With Lemma 12, we can prove existence of global in time solutions with an exponential weight using exactly the same argument as in the last section of [ 11 ].”
Boltzmann diffusive limit beyond the Navier‐Stokes approximation (2006, background): “5) and applying a standard continuity argument (see [22]), we thus deduce (2.”
Almost Exponential Decay Near Maxwellian (2006, unknown): “Mathematics Subject Classification 82B40; 82C40; 82D05; 82D10.”
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, unknown): “This is the case in a close-to-equilibrium setting, as shown in a beautiful recent series of works by Guo [33, 32, 34 ], treating both hard and soft potentials with cuto on one hand, and the Landau equation (with soft potentials”
Decay of Dissipative Equations and Negative Sobolev Spaces (2011, methodology): “On the other hand, some analogous theorems of global existence and decay rate of the solutions to the Boltzmann equation with forces have also been established; see [34, 33, 6] for the Boltzmann equation with external forces, [7, 36, 35, 3] for the Vlasov-Poisson-Boltzmann system and [8, 30, 14, 4] ”