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From Boltzmann to incompressible Navier-...

Briant, Marc...

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From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight by Briant, Marc ( Author )

Content Provider	Lemonjar Open Access
Publisher	N.A
Publication Date	15-12-2014
Summary	We study the Boltzmann equation on the d-dimensional torus in a perturbative setting around a global equilibrium under the Navier-Stokes linearisation. We use a recent functional analysis breakthrough to prove that the linear part of the equation generates a C0-semigroup with exponential decay in Lebesgue and Sobolev spaces with polynomial weight, independently on the Knudsen number. Finally we show a Cauchy theory and an exponential decay for the perturbed Boltzmann equation, uniformly in the Knudsen number, in Sobolev spaces with polynomial weight. The polynomial weight is almost optimal and furthermore, this result only requires derivatives in the space variable and allows to connect to solutions to the incompressible Navier-Stokes equations in these spaces.
ISBN	-
Item Type	Article
File Type	pdf
File Size	36.88 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	https://arxiv.org/abs/1412.4653

Citation

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AMA 11th EditionReferences

Briant, Marc. From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. N.A. December 15, 2014. Accessed October 02, 2025. https://online.provdatabase.com/cite/18220

APA 7th EditionReferences

Briant, Marc. (2014). From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. N.A. https://online.provdatabase.com/cite/18220

Chicago 17th EditionReferences

Briant, Marc. From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. N.A. 2014. https://online.provdatabase.com/cite/18220

HarvardReferences

Briant, Marc. (2014). From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. [Online]. N.A. Available from: https://online.provdatabase.com/cite/18220. (Accessed 02 October 2025).

Harvard AustraliaReferences

Briant, Marc, 2014, From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight, N.A, viewed 02 October 2025, <https://online.provdatabase.com/cite/18220>

MLA 9th EditionWorks Cited

Briant, Marc. From Boltzmann to incompressible Navier-Stokes in Sobolev spaces with polynomial weight. N.A, 2014. PROV Database, https://online.provdatabase.com/cite/18220.

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