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- W2908246981 abstract "This chapter focuses on the classical models of fluid mechanics. It introduces the Boltzmann equation and discusses its structure and main formal properties. The dimensionless form of the Boltzmann equation and its main scaling parameters are discussed in the chapter. It discusses in detail the formal derivation of the most classical partial differential equations (PDEs) of fluid mechanics from the Boltzmann equation by several different methods. The known mathematical results on the Cauchy problem for the PDEs of fluid mechanics and the-state-of-the-art on the existence theory for the Boltzmann equation are reviewed in the chapter. It focuses on compactness methods, leading to global results, and especially the derivation of global weak solutions of the incompressible Navier–Stokes equations from renormalized solutions of the Boltzmann equation. In some models that can be found in the literature, the “viscous heating” term is absent from the temperature equation. Whether the “viscous heating” term should be taken into account or not depends in fact on the relative size of the fluctuations of velocity field about its average value and of the fluctuations of temperature field about its average values." @default.
- W2908246981 created "2019-01-11" @default.
- W2908246981 creator A5052847352 @default.
- W2908246981 date "2005-01-01" @default.
- W2908246981 modified "2023-10-01" @default.
- W2908246981 title "The Boltzmann Equation and Its Hydrodynamic Limits" @default.
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- W2908246981 doi "https://doi.org/10.1016/s1874-5717(06)80006-x" @default.
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