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- W2904706295 abstract "We characterize the well known self-similar Blasius profiles, $[bar{u}, bar{v}]$, as downstream attractors to solutions $[u,v]$ to the 2D, stationary Prandtl system. It was established in cite{Serrin} that $| u - bar{u}|_{L^infty_y} rightarrow 0$ as $x rightarrow infty$. Our result furthers cite{Serrin} in the case of localized data near Blasius by establishing convergence in stronger norms and by characterizing the decay rates. Central to our analysis is a division estimate, in turn based on the introduction of a new quantity, $Omega$, which is globally nonnegative precisely for Blasius solutions. Coupled with an energy cascade and a new weighted Nash-type inequality, these ingredients yield convergence of $u - bar{u}$ and $v - bar{v}$ at the essentially the sharpest expected rates in $W^{k,p}$ norms." @default.
- W2904706295 created "2018-12-22" @default.
- W2904706295 creator A5060891659 @default.
- W2904706295 date "2018-12-10" @default.
- W2904706295 modified "2023-09-27" @default.
- W2904706295 title "On Global-in-$x$ Stability of Blasius Profiles" @default.
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- W2904706295 hasPublicationYear "2018" @default.
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