Well-posedness of The Prandtl Equation in Sobolev Spaces
| hal.structure.identifier | Institut de Recherche de l'Ecole Navale [IRENAV] | |
| dc.contributor.author | ALEXANDRE, Radjesvarane | |
| hal.structure.identifier | Departement of Mathematics | |
| dc.contributor.author | WANG, Ya-Guang | |
| hal.structure.identifier | Laboratoire de Mathématiques Raphaël Salem [LMRS] | |
| dc.contributor.author | XU, Chao-Jiang | |
| hal.structure.identifier | Department of mathematics [Pr.] | |
| dc.contributor.author | YANG, Tong | |
| dc.date.accessioned | 2021-05-14T10:04:46Z | |
| dc.date.available | 2021-05-14T10:04:46Z | |
| dc.date.created | 2012-03-27 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/78516 | |
| dc.description.abstractEn | We develop a new approach to study the well-posedness theory of the Prandtl equation in Sobolev spaces by using a direct energy method under a monotonicity condition on the tangential velocity field instead of using the Crocco transformation. Precisely, we firstly investigate the linearized Prandtl equation in some weighted Sobolev spaces when the tangential velocity of the background state is monotonic in the normal variable. Then to cope with the loss of regularity of the perturbation with respect to the background state due to the degeneracy of the equation, we apply the Nash-Moser-Hormander iteration to obtain a well-posedness theory of classical solutions to the nonlinear Prandtl equation when the initial data is a small perturbation of a monotonic shear flow. | |
| dc.language.iso | en | |
| dc.subject.en | Prandtl equation | |
| dc.subject.en | well-posedness theory | |
| dc.subject.en | Sobolev spaces | |
| dc.subject.en | energy method | |
| dc.subject.en | monotonic velocity field | |
| dc.subject.en | Nash-Moser-Hormander iteration | |
| dc.title.en | Well-posedness of The Prandtl Equation in Sobolev Spaces | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 1203.5991 | |
| bordeaux.hal.laboratories | Institut de Mécanique et d’Ingénierie de Bordeaux (I2M) - UMR 5295 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.institution | INRAE | |
| bordeaux.institution | Arts et Métiers | |
| hal.identifier | hal-00682867 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00682867v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=ALEXANDRE,%20Radjesvarane&WANG,%20Ya-Guang&XU,%20Chao-Jiang&YANG,%20Tong&rft.genre=preprint |
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