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

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 \cite{Ch04, 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.

References in corpus (2)

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

Cited by in corpus (7)

• Almost global existence for the Prandtl boundary layer equations
• On the ill-posedness of the Prandtl equations in three space dimensions
• Well-posedness in Gevrey function space for the three-dimensional Prandtl equations
• Long time well-posdness of the Prandtl equations in Sobolev space
• Separation of the two-dimensional unsteady Prandtl boundary layers under an adverse pressure gradient
• Well-Posedness of the Nonlinear Unsteady Prandtl Equations with Robin Boundary Condition in Weighted Sobolev Spaces
• Full Regularity and Well-Posedness of the Nonlinear Unsteady Prandtl Equations with Robin or Dirichlet Boundary Condition