L(p)-estimates of the Boltzmann equation around a traveling local Maxwellian

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In this paper, we are interested in the LP-estimates of the Boltzmann equation in the case that the distribution function stays around a traveling local Maxwellian. For this, we divide both sides of the Boltzmann equation by the velocity distribution function with a fractional exponent and reformulate the Boltzmann equation into a regularized one. This amounts to endowing additional integrability on the collision kernel, which in turn enables us to apply simple Holder type inequalities. Our results cover the whole range of Lebesgue exponents: 0 < p <= infinity (C) 2011 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2011-07
Language
English
Article Type
Article
Keywords

GLOBAL EXISTENCE; EXTERNAL FORCES; STABILITY; VACUUM; GAS; UNIQUENESS; SPACE

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.251, no.1, pp.45 - 57

ISSN
0022-0396
DOI
10.1016/j.jde.2011.03.001
URI
http://hdl.handle.net/10203/94294
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