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- Title
Almost Global Existence for the Prandtl Boundary Layer Equations.
- Authors
Ignatova, Mihaela; Vicol, Vlad
- Abstract
We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H space 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 $${\varepsilon}$$ of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time $${T_{\varepsilon} \geqq {\rm exp}(\varepsilon^{-1} / {\rm log}(\varepsilon^{-1}))}$$ .
- Subjects
BOUNDARY layer equations; H-spaces; EULER equations; EXISTENCE theorems; CAUCHY problem
- Publication
Archive for Rational Mechanics & Analysis, 2016, Vol 220, Issue 2, p809
- ISSN
0003-9527
- Publication type
Article
- DOI
10.1007/s00205-015-0942-2