REVIEW 2 cited by
Well-posedness in Gevrey function space for the three-dimensional Prandtl equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
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].
Forward citations
Cited by 2 Pith papers
-
Long time well-posedness for the 3D Prandtl boundary layer equations with a special structure
The 3D Prandtl equations with the special structure v=Ku admit unique stable solutions on arbitrarily long time intervals when the initial data are small monotone perturbations of a shear profile.
-
Prandtl Equations and Related Boundary Layer Equations
The book claims new well-posedness theorems for Prandtl and MHD boundary layer equations, but the provided text only shows the survey portion.
Discussion (0). Continue with ORCID to comment.