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Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation

hal.structure.identifierInstitut de Recherche de l'Ecole Navale [IRENAV]
dc.contributor.authorALEXANDRE, Radjesvarane
hal.structure.identifierGraduate School of Human and Environmental Studies
dc.contributor.authorMORIMOTO, Yoshinori
hal.structure.identifierretaite [Mr.]
dc.contributor.authorUKAI, Seiji
hal.structure.identifierLaboratoire de Mathématiques Raphaël Salem [LMRS]
dc.contributor.authorXU, Chao-Jiang
hal.structure.identifierDepartment of mathematics [Pr.]
dc.contributor.authorYANG, Tong
dc.date.accessioned2021-05-14T09:57:54Z
dc.date.available2021-05-14T09:57:54Z
dc.date.issued2010
dc.identifier.issn0003-9527
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/77909
dc.description.abstractEnThe Boltzmann equation without Grad’s angular cutoff assumption is believedto have a regularizing effect on the solutions because of the non-integrable angularsingularity of the cross-section. However, even though this has been justifiedsatisfactorily for the spatially homogeneous Boltzmann equation, it is still basicallyunsolved for the spatially inhomogeneous Boltzmann equation. In this paper,by sharpening the coercivity and upper bound estimates for the collision operator,establishing the hypo-ellipticity of the Boltzmann operator based on a generalizedversion of the uncertainty principle, and analyzing the commutators between thecollision operator and some weighted pseudo-differential operators, we prove theregularizing effect in all (time, space and velocity) variables on the solutions whensome mild regularity is imposed on these solutions. For completeness, we also showthat when the initial data has this mild regularity and a Maxwellian type decay inthe velocity variable, there exists a unique local solution with the same regularity,so that this solution acquires the C∞ regularity for any positive time.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enRegularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation
dc.typeArticle de revue
dc.identifier.doi10.1007/s00205-010-0290-1
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.identifier.arxiv0909.1229
bordeaux.journalArchive for Rational Mechanics and Analysis
bordeaux.page39-123
bordeaux.volume198
bordeaux.hal.laboratoriesInstitut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.institutionINRAE
bordeaux.institutionArts et Métiers
bordeaux.peerReviewedoui
hal.identifierhal-01116729
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01116729v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Archive%20for%20Rational%20Mechanics%20and%20Analysis&rft.date=2010&rft.volume=198&rft.spage=39-123&rft.epage=39-123&rft.eissn=0003-9527&rft.issn=0003-9527&rft.au=ALEXANDRE,%20Radjesvarane&MORIMOTO,%20Yoshinori&UKAI,%20Seiji&XU,%20Chao-Jiang&YANG,%20Tong&rft.genre=article


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