Global Well-Posedness in Spatially Critical Besov Space for the Boltzmann Equation

Renjun Duan; Shuangqian Liu; Jiang Xu

doi:10.1007/s00205-015-0940-4

Global Well-Posedness in Spatially Critical Besov Space for the Boltzmann Equation

Renjun Duan^*
, Shuangqian Liu
, Jiang Xu

^*Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

23 Citations (Scopus)

Abstract

The unique global strong solution in the Chemin–Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in a perturbation framework. Such a solution space is of critical regularity with respect to the spatial variable, and it can capture the intrinsic properties of the Boltzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood–Paley theory.

Original language	English
Pages (from-to)	711-745
Journal	Archive for Rational Mechanics and Analysis
Volume	220
Issue number	2
DOIs	https://doi.org/10.1007/s00205-015-0940-4
Publication status	Published - 1 May 2016
Externally published	Yes

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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abstract = "The unique global strong solution in the Chemin–Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in a perturbation framework. Such a solution space is of critical regularity with respect to the spatial variable, and it can capture the intrinsic properties of the Boltzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood–Paley theory.",

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AU - Duan, Renjun

AU - Liu, Shuangqian

AU - Xu, Jiang

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N2 - The unique global strong solution in the Chemin–Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in a perturbation framework. Such a solution space is of critical regularity with respect to the spatial variable, and it can capture the intrinsic properties of the Boltzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood–Paley theory.

AB - The unique global strong solution in the Chemin–Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in a perturbation framework. Such a solution space is of critical regularity with respect to the spatial variable, and it can capture the intrinsic properties of the Boltzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood–Paley theory.

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DO - 10.1007/s00205-015-0940-4

M3 - RGC 21 - Publication in refereed journal

SN - 0003-9527

VL - 220

SP - 711

EP - 745

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

IS - 2

ER -

Global Well-Posedness in Spatially Critical Besov Space for the Boltzmann Equation

Abstract

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