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

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arxiv 1708.08217 v4 pith:NN6PCBVK submitted 2017-08-28 math.AP

classification math.AP
keywords gevreyspaceequationsfieldfunctionprandtlsystemthree-dimensional
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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].

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Long time well-posedness for the 3D Prandtl boundary layer equations with a special structure

    math.AP 2024-11 conditional novelty 6.0 of 10

    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.

  2. Prandtl Equations and Related Boundary Layer Equations

    math.AP 2024-11 unverdicted novelty 5.0 of 10

    The book claims new well-posedness theorems for Prandtl and MHD boundary layer equations, but the provided text only shows the survey portion.

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