Long time well-posdness of Prandtl system with small and analytic initial data

2014/09/05 by Ping Zhang, Zhifei Zhang, Zhang, Ping +1 · 3 citations
Mathematics · #35Q30 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.1648

openalex publication_date 2014/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the long time existence and uniqueness of small solution to d, for d=2,3, dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that d dimensional Prandtl system has a unique solution with the life-span of which is greater than \e^-\f43 if both the initial data and the value on the boundary of the tangential velocity of the outflow are of size \e. We mention that the tool developed in \citeCh04, CGP to make the analytical type estimates and the special structure of the nonlinear terms to this system play an essential role in the proof of this result.

Citations

• On the local well-posedness of the Prandtl and the hydrostatic Euler\n equations with multiple monotonicity regions

Cited by

• Gevrey well-posedness of the hydrostatic MHD-wave system
• Well-posedness of the compressible boundary layer equations with analytic initial data
• Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

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