Geodesic
Boundary Layer Expansions for the Stationary Navier-Stokes Equations
Ars Inveniendi Analytica (2021).

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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 $x \rightarrow \infty$.
Publié le :
DOI : 10.15781/64dc-7z92 
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     author = {Sameer Iyer and Nader Masmoudi},
     title = {Boundary {Layer} {Expansions} for the {Stationary} {Navier-Stokes} {Equations}},
     journal = {Ars Inveniendi Analytica},
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     year = {2021},
     doi = {10.15781/64dc-7z92},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.15781/64dc-7z92/}
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Sameer Iyer; Nader Masmoudi. Boundary Layer Expansions for the Stationary Navier-Stokes Equations. Ars Inveniendi Analytica (2021). doi : 10.15781/64dc-7z92. http://geodesic.mathdoc.fr/articles/10.15781/64dc-7z92/

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