Existence and sharp localization in velocity of small amplitude Boltzman shocks
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | METIVIER, Guy | |
| hal.structure.identifier | Department of Mathematics IU | |
| dc.contributor.author | ZUMBRUN, Kevin | |
| dc.date.accessioned | 2024-04-04T02:23:02Z | |
| dc.date.available | 2024-04-04T02:23:02Z | |
| dc.date.created | 2009 | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 1937-5093 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189695 | |
| dc.description.abstractEn | Using a weighted $H^s$-contraction mapping argument based on the macro-micro decomposition of Liu and Yu, we give an elementary proof of existence, with sharp rates of decay and distance from the Chapman--Enskog approximation, of small-amplitude shock profiles of the Boltzmann equation with hard-sphere potential, recovering and slightly sharpening results obtained by Caflisch and Nicolaenko using different techniques. A key technical point in both analyses is that the linearized collision operator $L$ is negative definite on its range, not only in the standard square-root Maxwellian weighted norm for which it is self-adjoint, but also in norms with nearby weights. Exploring this issue further, we show that $L$ is negative definite on its range in a much wider class of norms including norms with weights asymptotic nearly to a full Maxwellian rather than its square root. This yields sharp localization in velocity at near-Maxwellian rate, rather than the square-root rate obtained in previous analyses. | |
| dc.language.iso | en | |
| dc.publisher | AIMS | |
| dc.subject.en | shock profiles | |
| dc.subject.en | relaxation | |
| dc.subject.en | macro-micro decomposition | |
| dc.subject.en | Chapman-Enskog approximation | |
| dc.subject.en | energy methods | |
| dc.title.en | Existence and sharp localization in velocity of small amplitude Boltzman shocks | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Kinetic and Related Models | |
| bordeaux.page | pp 209--231 | |
| bordeaux.volume | 2 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00777124 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00777124v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Kinetic%20and%20Related%20Models&rft.date=2009&rft.volume=2&rft.spage=pp%20209--231&rft.epage=pp%20209--231&rft.eissn=1937-5093&rft.issn=1937-5093&rft.au=METIVIER,%20Guy&ZUMBRUN,%20Kevin&rft.genre=article |
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