Well-Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption

作者：Li, Wei-Xi^*; Masmoudi, Nader; Yang, Tong

来源：Communications on Pure and Applied Mathematics, 2022, 75(8): 1755-1797.

DOI：10.1002/cpa.21989

• ILL-POSEDNESS
• INVISCID LIMIT
• INSTABILITY
• EXPANSIONS
• EXISTENCE
• STABILITY
• EULER
• FLOWS

We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three-dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three-dimensional instabilities in the system leading to ill-posedness are not worse than the two-dimensional ones.

• 单位
  武汉大学