On the local existence of analytic solutions to the Prandtl boundary layer equations

By Igor Kukavica, Vlad Vicol. 2013

120 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8086f7646efa2be6a3927cc76b61b886a75c9f98

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In Applied Mathematics

In Mathematical Physics

In Numerical Analysis

Citations in the corpus

Gevrey stability of Prandtl expansions for 2-dimensional Navier–Stokes flows (2016, unknown): “ • Without themonotonicityassumption, the situationis muchlessfavorable. Existenceof local in time analytic solutions, for analytic initial data, was shown by Sammartino and Caﬂisch in [22], see also [16, 14]. Article [4] by the ﬁrst author and Dormy established the ill-posedness of (1.0.3) in the S”
Well-posedness of the hydrostatic Navier–Stokes equations (2018, background): “ing out of reach. If conﬁrmed, it would emphasize the destabilizing role of viscosity. • We loose on the radius τof Gevrey regularity, going from τ0 to τ1 in positive time. This loss is very standard [39, 24, 25, 14]. • Besides the Gevrey regularity assumption (2.1), the key assumption is infΩ ∂2 yu”
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”
Well-posedness for the Prandtl system without analyticity or monotonicity (2013, background): “would require some modifications, see [15] for a similar problem.”
Local‐in‐Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods (2012, background): “In full generality, these questions are still open except in the analytic case where (a)–(c) can be proved [21, 22, 33, 34].”
On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane (2012, background): “Without the monotonicity conditions so far we need the analyticity of the initial data to show the local-in-time solvability of the Prandtl equations [4, 49], and this analyticity is in fact required only in the tangential direction [29, 30].”
Well-posedness of the Prandtl equation without any structural assumption (2018, methodology): “One can also mention [22], where this difficulty is overcome by a clever change of variables, which is reminiscent of the method of characteristics and allows to remove the bad part of the convection term from the equation.”