Decay and Continuity of the Boltzmann Equation in Bounded Domains
Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow, boun...
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| Veröffentlicht in: | Archive for rational mechanics and analysis 2010-09, Vol.197 (3), p.713-809 |
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| creator | Guo, Yan |
| description | Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow, bounce-back reflection, specular reflection and diffuse reflection. We establish exponential decay in the
L
∞
norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is based on a new
L
2
decay theory and its interplay with delicate
L
∞
decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary. |
| doi_str_mv | 10.1007/s00205-009-0285-y |
| format | Article |
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L
∞
norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is based on a new
L
2
decay theory and its interplay with delicate
L
∞
decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary.</description><identifier>ISSN: 0003-9527</identifier><identifier>EISSN: 1432-0673</identifier><identifier>DOI: 10.1007/s00205-009-0285-y</identifier><identifier>CODEN: AVRMAW</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Classical Mechanics ; Classical statistical mechanics ; Complex Systems ; Exact sciences and technology ; Fluid- and Aerodynamics ; Kinetic theory ; Mathematical and Computational Physics ; Physics ; Physics and Astronomy ; Statistical physics, thermodynamics, and nonlinear dynamical systems ; Theoretical</subject><ispartof>Archive for rational mechanics and analysis, 2010-09, Vol.197 (3), p.713-809</ispartof><rights>Springer-Verlag 2009</rights><rights>2015 INIST-CNRS</rights><rights>Springer-Verlag 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c345t-bcba25043b3ba6cb6e1f3be0beced6f5fd6e812d4b9b9303032abe6f18cee1b3</citedby><cites>FETCH-LOGICAL-c345t-bcba25043b3ba6cb6e1f3be0beced6f5fd6e812d4b9b9303032abe6f18cee1b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00205-009-0285-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00205-009-0285-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,778,782,27911,27912,41475,42544,51306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23050638$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Guo, Yan</creatorcontrib><title>Decay and Continuity of the Boltzmann Equation in Bounded Domains</title><title>Archive for rational mechanics and analysis</title><addtitle>Arch Rational Mech Anal</addtitle><description>Boundaries occur naturally in kinetic equations, and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: in-flow, bounce-back reflection, specular reflection and diffuse reflection. We establish exponential decay in the
L
∞
norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is based on a new
L
2
decay theory and its interplay with delicate
L
∞
decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary.</description><subject>Classical Mechanics</subject><subject>Classical statistical mechanics</subject><subject>Complex Systems</subject><subject>Exact sciences and technology</subject><subject>Fluid- and Aerodynamics</subject><subject>Kinetic theory</subject><subject>Mathematical and Computational Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Statistical physics, thermodynamics, and nonlinear dynamical 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L
∞
norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set at the boundary. Our contribution is based on a new
L
2
decay theory and its interplay with delicate
L
∞
decay analysis for the linearized Boltzmann equation in the presence of many repeated interactions with the boundary.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s00205-009-0285-y</doi><tpages>97</tpages></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Classical Mechanics Classical statistical mechanics Complex Systems Exact sciences and technology Fluid- and Aerodynamics Kinetic theory Mathematical and Computational Physics Physics Physics and Astronomy Statistical physics, thermodynamics, and nonlinear dynamical systems Theoretical |
| title | Decay and Continuity of the Boltzmann Equation in Bounded Domains |
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