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Article: Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods

TitleLocal-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
Authors
Issue Date2015
Citation
Communications on Pure and Applied Mathematics, 2015, v. 68, n. 10, p. 1683-1741 How to Cite?
Abstract© 2015 Wiley Periodicals, Inc.We prove local existence and uniqueness for the two-dimensional Prandtl system in weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not use the Crocco transform or any change of variables. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property that is valid under the monotonicity assumption. To construct the solution, we use a regularization of the system that preserves this nonlinear structure. This new nonlinear structure may give some insight into the convergence properties from the Navier-Stokes system to the Euler system when the viscosity goes to 0.
Persistent Identifierhttp://hdl.handle.net/10722/228224
ISSN
2015 Impact Factor: 3.617
2015 SCImago Journal Rankings: 4.177

 

DC FieldValueLanguage
dc.contributor.authorMasmoudi, Nader-
dc.contributor.authorWong, Tak Kwong-
dc.date.accessioned2016-08-01T06:45:30Z-
dc.date.available2016-08-01T06:45:30Z-
dc.date.issued2015-
dc.identifier.citationCommunications on Pure and Applied Mathematics, 2015, v. 68, n. 10, p. 1683-1741-
dc.identifier.issn0010-3640-
dc.identifier.urihttp://hdl.handle.net/10722/228224-
dc.description.abstract© 2015 Wiley Periodicals, Inc.We prove local existence and uniqueness for the two-dimensional Prandtl system in weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not use the Crocco transform or any change of variables. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property that is valid under the monotonicity assumption. To construct the solution, we use a regularization of the system that preserves this nonlinear structure. This new nonlinear structure may give some insight into the convergence properties from the Navier-Stokes system to the Euler system when the viscosity goes to 0.-
dc.languageeng-
dc.relation.ispartofCommunications on Pure and Applied Mathematics-
dc.titleLocal-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods-
dc.typeArticle-
dc.description.natureLink_to_subscribed_fulltext-
dc.identifier.doi10.1002/cpa.21595-
dc.identifier.scopuseid_2-s2.0-84938958766-
dc.identifier.volume68-
dc.identifier.issue10-
dc.identifier.spage1683-
dc.identifier.epage1741-
dc.identifier.eissn1097-0312-

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