Acoustic and Stokes limits for the Boltzmann equation

Claude Bardos; François Golse; C. David Levermore

doi:10.1016/S0764-4442(98)80154-7

Acoustic and Stokes limits for the Boltzmann equation

Claude Bardos
, François Golse
, C. David Levermore

Research output: Contribution to journal › Article › peer-review

Abstract

The Boltzmann equation is considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L¹) to a unique limit governed by a solution of the acoustic or Stokes equations, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L² initial data of the acoustic or Stokes equations. The associated conservation laws are recovered in the limit.

Translated title of the contribution	Les limites acoustique et de Stokes de l'équation de Boltzmann
Original language	English
Pages (from-to)	323-328
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	327
Issue number	3
DOIs	https://doi.org/10.1016/S0764-4442(98)80154-7
Publication status	Published - 1 Jan 1998
Externally published	Yes

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title = "Acoustic and Stokes limits for the Boltzmann equation",

abstract = "The Boltzmann equation is considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L1) to a unique limit governed by a solution of the acoustic or Stokes equations, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L2 initial data of the acoustic or Stokes equations. The associated conservation laws are recovered in the limit.",

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AU - Golse, François

AU - Levermore, C. David

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N2 - The Boltzmann equation is considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L1) to a unique limit governed by a solution of the acoustic or Stokes equations, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L2 initial data of the acoustic or Stokes equations. The associated conservation laws are recovered in the limit.

AB - The Boltzmann equation is considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in L1) to a unique limit governed by a solution of the acoustic or Stokes equations, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given L2 initial data of the acoustic or Stokes equations. The associated conservation laws are recovered in the limit.

U2 - 10.1016/S0764-4442(98)80154-7

DO - 10.1016/S0764-4442(98)80154-7

M3 - Article

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SN - 0764-4442

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EP - 328

JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 3

ER -

Acoustic and Stokes limits for the Boltzmann equation

Abstract

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