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Article: Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods
Title | Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods |
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Authors | |
Issue Date | 2015 |
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 Identifier | http://hdl.handle.net/10722/228224 |
ISSN | 2023 Impact Factor: 3.1 2023 SCImago Journal Rankings: 4.188 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Masmoudi, Nader | - |
dc.contributor.author | Wong, Tak Kwong | - |
dc.date.accessioned | 2016-08-01T06:45:30Z | - |
dc.date.available | 2016-08-01T06:45:30Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | Communications on Pure and Applied Mathematics, 2015, v. 68, n. 10, p. 1683-1741 | - |
dc.identifier.issn | 0010-3640 | - |
dc.identifier.uri | http://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.language | eng | - |
dc.relation.ispartof | Communications on Pure and Applied Mathematics | - |
dc.title | Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/cpa.21595 | - |
dc.identifier.scopus | eid_2-s2.0-84938958766 | - |
dc.identifier.volume | 68 | - |
dc.identifier.issue | 10 | - |
dc.identifier.spage | 1683 | - |
dc.identifier.epage | 1741 | - |
dc.identifier.eissn | 1097-0312 | - |
dc.identifier.isi | WOS:000359670800001 | - |
dc.identifier.issnl | 0010-3640 | - |