From the Boltzmann Equations¶to the Equations of¶Incompressible Fluid Mechanics, I

By Pierre-Louis Lions, Nader Masmoudi. 2001

185 citations recorded by the source corpus.

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In Applied Mathematics

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Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory (2002, background): “I also warmly thank L. Arkeryd, E. Caglioti, C. Cercignani, L. Desvillettes, X. Lu, F. Malrieu, N. Masmoudi, M. Pulvirenti, G. Toscani for providing remarks and corrections, and J.-F. Coulombel for his job of tracking misprints.”
On the Boltzmann equation for long‐range interactions (2002, result): “Even though, up to this date, many open questions remain on the subject of renormalized solutions (uniqueness, smoothness, energy conservation), the DiPerna-Lions result has enabled the study of several physical phenomena, in particular the hydrodynamical limit whose analysis was later performed by ”
From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain (2003, background): “[2, 10, 12, 13, 14, 15] with the present analysis at the boundary allows the NavierStokes limit of the Boltzmann equation to be derived in a bounded domain.”
Relative Entropy and the Stability of Shocks and Contact Discontinuities for Systems of Conservation Laws with non-BV Perturbations (2010, methodology): “For incompressible limits, see Bardos, Golse, Levermore [1, 2], Lions and Masmoudi [27], Saint Raymond et al. [20, 37, 32, 36].”
Mathematical tools for kinetic equations (2004, background): “In a series of papers by Bardos, Golse, Levermore and Saint-Raymond [9], [68], and by Lions and Masmoudi [89], the incompressible Navier-Stokes limit has been considered.”
Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws (2015, methodology): “Applications of the relative entropy method in this context began with the work of Yau [55] and have been studied in various context (See for instance [2, 3, 7, 8, 23, 26, 34, 37, 38, 42]).”
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation (2005, background): “2 This rule of course admits some exceptions, for instance the study of sound waves in the incompressible limit, see [6,40,29] or the survey in [57].”
Global existence for the Euler-Maxwell system (2011, background): “We refer to [23, 16, 21] for more about hydrodynamic limits.”