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Well-posedness for the Prandtl system without analyticity or monotonicity. (Caractère bien posé de l’équation de Prandtl sans monotonie ou analycité.) (English. French summary) Zbl 1347.35201

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.

MSC:

35Q35 PDEs in connection with fluid mechanics
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D05 Navier-Stokes equations for incompressible viscous fluids
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
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