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- W3017201327 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 Serrin (Proc R Soc Lond A 299:491–507, 1967) using maximum principle techniques that $$Vert u - {bar{u}}Vert _{L^infty _y} rightarrow 0$$ as $$x rightarrow infty $$. In the case of localized data near Blasius, this paper provides an energy based proof of asymptotic stability. Central to our analysis is a new weighted “quotient estimate” which couples with a higher order, nonlinear energy cascade. Similar quotient estimates have played a crucial role in establishing the validity of the inviscid Prandtl layer expansion in Guo and Iyer (Validity of steady Prandtl layer expansions. arXiv:1805.05891 2018)." @default.
- W3017201327 created "2020-04-24" @default.
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- W3017201327 date "2020-04-15" @default.
- W3017201327 modified "2023-10-16" @default.
- W3017201327 title "On Global-in-x Stability of Blasius Profiles" @default.
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- W3017201327 doi "https://doi.org/10.1007/s00205-020-01523-5" @default.
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