Almost Global Existence for the Prandtl Boundary Layer Equations

Mihaela Ignatova; Vlad Vicol

doi:10.1007/s00205-015-0942-2

Almost Global Existence for the Prandtl Boundary Layer Equations

Mihaela Ignatova
, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

93 Scopus citations

Abstract

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H¹space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within (Formula presented.) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time (Formula presented.).

Original language	English (US)
Pages (from-to)	809-848
Number of pages	40
Journal	Archive for Rational Mechanics and Analysis
Volume	220
Issue number	2
DOIs	https://doi.org/10.1007/s00205-015-0942-2
State	Published - May 2016

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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abstract = "We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within (Formula presented.) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time (Formula presented.).",

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AB - We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H1space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within (Formula presented.) of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time (Formula presented.).

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Almost Global Existence for the Prandtl Boundary Layer Equations

Abstract

All Science Journal Classification (ASJC) codes

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