Boundary Layer Expansions for the Stationary Navier-Stokes Equations

Abstract

This is the first part of a two paper sequence in which we prove the global-in-x stability of the classical Prandtl boundary layer for the 2D, stationary Navier-Stokes equations. In this part, we provide a construction of an approximate Navier-Stokes solution, obtained by a classical Euler- Prandtl asymptotic expansion. We develop here sharp decay estimates on these quantities. Of independent interest, we establish \textit{without} using the classical von-Mise change of coordinates, proofs of global in x regularity of the Prandtl system. The results of this paper are used in the second part of this sequence, [IM20] (arXiv:2008.12347), to prove the asymptotic stability of the boundary layer as $\eps \rightarrow 0$ and $x\to \infty$.

arXiv commentCompanion paper to arXiv:2008.12347. Accepted version in journal style

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Cited by in corpus (1)

• Global-in-$x$ stability of Prandtl layer expansions for steady magnetohydrodynamics flows over a moving plate