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Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay
- Source :
- Journal de Mathématiques Pures et Appliquées. 108:150-162
- Publication Year :
- 2017
- Publisher :
- Elsevier BV, 2017.
-
Abstract
- Motivated by the paper Gerard-Varet and Dormy (2010) [6] [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in [6] to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations.
- Subjects :
- Applied Mathematics
General Mathematics
010102 general mathematics
Mathematical analysis
Prandtl number
Mathematics::Analysis of PDEs
01 natural sciences
Physics::Fluid Dynamics
010101 applied mathematics
Sobolev space
symbols.namesake
Inviscid flow
symbols
0101 mathematics
Exponential decay
Shear flow
Approximate solution
Ill posedness
Mathematics
Variable (mathematics)
Subjects
Details
- ISSN :
- 00217824
- Volume :
- 108
- Database :
- OpenAIRE
- Journal :
- Journal de Mathématiques Pures et Appliquées
- Accession number :
- edsair.doi...........a878eed9c170d21337f090920cb70322