Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Validity of Steady Prandtl Layer Expansions   Let the viscosity $\varepsilon \rightarrow 0$ for the 2D steady Navier-Stokes
equations in the region $0\leq x\leq L$ and $0\leq y<\infty$ with no slip
boundary conditions at $y=0$. For $L<<1$, we justify the validity of the steady
Prandtl layer expansion for scaled Prandtl layers, including the celebrated
Blasius boundary layer. Our uniform estimates in $\varepsilon$ are achieved
through a fixed-point scheme: \begin{equation*} [u^{0}, v^0]
\overset{\text{DNS}^{-1}}{\longrightarrow }v\overset{\mathcal{L}^{-1}}{
\longrightarrow }[u^{0}, v^0] \label{fixedpoint} \end{equation*} for solving
the Navier-Stokes equations, where $[u^{0}, v^0]$ are the tangential and normal
velocities at $x=0,$ DNS stands for $\partial _{x}$ of the vorticity equation
for the normal velocity $v$, and $\mathcal{L}$ the compatibility ODE for
$[u^{0}, v^0]$ at $x=0.$

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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph