Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 150-162 |
| Journal / Publication | Journal des Mathematiques Pures et Appliquees |
| Volume | 108 |
| Issue number | 2 |
| Online published | 2 Nov 2016 |
| Publication status | Published - Aug 2017 |
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Abstract
Motivated by the paper Gérard-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.
Research Area(s)
- General decay, Linear instability, Prandtl equations, Shear flow
Citation Format(s)
Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay. / Liu, Cheng-Jie; Yang, Tong.
In: Journal des Mathematiques Pures et Appliquees, Vol. 108, No. 2, 08.2017, p. 150-162.Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
