Well-posedness for the Prandtl system without analyticity or monotonicity (Q2788607)
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scientific article; zbMATH DE number 6543144
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Well-posedness for the Prandtl system without analyticity or monotonicity |
scientific article; zbMATH DE number 6543144 |
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Well-posedness for the Prandtl system without analyticity or monotonicity (English)
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19 February 2016
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boundary layer
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Prandtl system
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Navier-Stokes equations
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Gevrey spaces
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This article gives a proof that the Cauchy problem of the 2D Prandtl system on \(\mathbb T\times\mathbb R_+\) has a unique, local-in-time solution for initial data \(u_0=u_0(x,y)\) which belong to the Gevrey class \(7/4\) with respect to the \(x\)-variable. The proof of this result relies on a priori estimates for an anisotropic energy functional and on a suitable regularization of the Prandtl system.
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