Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

2017/08/28 by Wei‐Xi Li, Tong Yang, Li, Wei-Xi +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1708.08217

openalex publication_date 2017/08/28 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28

Abstract

In the paper, we study the three-dimensional Prandtl equations without any monotonicity condition on the velocity field. We prove that when one tangential component of the velocity field has a single curve of non-degenerate critical points with respect to the normal variable, the system is locally well-posed in the Gevrey function space with Gevrey index in ]1, 2]. The proof is based on some new observation of cancellation mechanism in the three space dimensional system in addition to those in the two-dimensional setting obtained in [1,7,19,22].

Citations

• Long time well-posdness of Prandtl system with small and analytic initial data
• Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical points
• Long time well-posdness of the Prandtl equations in Sobolev space

Related

• Well-posedness in Gevrey space for the Prandtl equations with non-degenerate critical points
• Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption
• Well-posedness for the Prandtl system without analyticity or\n monotonicity
• Gevrey well-posedness of quasi-linear hyperbolic Prandtl equations
• Gevrey well-posedness of the hyperbolic Prandtl equations