Gérard-Varet, David; Masmoudi, Nader 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 Ann. Sci. Éc. Norm. Supér. (4) 48, No. 6, 1273-1325 (2015). 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. Reviewer: Thomas Hagen (Memphis) Cited in 2 ReviewsCited in 88 Documents 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 Keywords:boundary layer; Prandtl system; Navier-Stokes equations; Gevrey spaces PDFBibTeX XMLCite \textit{D. Gérard-Varet} and \textit{N. Masmoudi}, Ann. Sci. Éc. Norm. Supér. (4) 48, No. 6, 1273--1325 (2015; Zbl 1347.35201) Full Text: DOI arXiv Link