Well-posedness of the Prandtl equation without any structural assumption

By Helge Dietert, Davdi Gerard-Varet. 2018

68 citations recorded by the source corpus.

We show the local in time well-posedness of the Prandtl equation for data with Gevrey $2$ regularity in $x$ and $H^1$ regularity in $y$. The main novelty of our result is that we do not make any assumption on the structure of the initial data: no monotonicity or hypothesis on the critical points. Moreover, our general result is optimal in terms of regularity, in view of the ill-posedness result of [9].

View Paper: https://www.semanticscholar.org/paper/39f291b6669b6429807f74d14d37c81a31fd46c4

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Citations in the corpus

Well‐Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption (2020, methodology): “Extending our result to the case of a general outer flow requires using some nontrivial weights similar to those in [9].”
Global existence and decay of solutions to Prandtl system with small analytic data. (2019, unknown): “This result was improved to be optimal in sense of [10] in [7] by Dietert and Gérvard-Varet.”
The Inviscid Limit for the Navier–Stokes Equations with Data Analytic Only Near the Boundary (2019, methodology): “We refer the reader to [1, 10, 17, 28, 35, 36, 37, 39, 47, 51, 52] for the well-posedness theory for the Prandtl equations, to [14, 26, 18, 38] for the identification of ill-posed regimes, and to [19, 20, 21, 22, 23] for recent works which show the invalidity of the Prandtl expansion at the level of”