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On Global-in-x Stability of Blasius Profiles


We characterize the well known self-similar Blasius profiles, \([{\bar{u}}, {\bar{v}}]\), as downstream attractors to solutions [uv] 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).

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Correspondence to Sameer Iyer.

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Communicated by P. Constantin

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S. Iyer Partially supported by NSF Grant DMS-1611695, DMS-1802940.

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Iyer, S. On Global-in-x Stability of Blasius Profiles. Arch Rational Mech Anal 237, 951–998 (2020).

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