ALEXANDRE, Radjesvarane; WANG, Ya-Guang; XU, Chao-Jiang; YANG, Tong

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ALEXANDRE, Radjesvarane
Institut de Recherche de l'Ecole Navale [IRENAV]

WANG, Ya-Guang
Departement of Mathematics

XU, Chao-Jiang
Laboratoire de Mathématiques Raphaël Salem [LMRS]

Langue

Document de travail - Pré-publication

Résumé en anglais

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.< Réduire

Mots clés en anglais

Prandtl equation

well-posedness theory

Sobolev spaces

energy method

monotonic velocity field

Nash-Moser-Hormander iteration

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Well-posedness of The Prandtl Equation in Sobolev Spaces

Langue

Résumé en anglais

Mots clés en anglais

URI

Origine

Unités de recherche