Dynamic stability for steady Prandtl solutions
Yan Guo, Yue Wang, Zhifei Zhang
TL;DR
This paper proves the stability of steady solutions to the Prandtl equation using an invariant set in Crocco transformation, demonstrating their orbital and asymptotic stability against certain monotone solutions.
Contribution
It introduces an invariant set approach in Crocco transformation to establish stability of Blasius-like steady states for the Prandtl equation.
Findings
Orbital stability of Blasius-like solutions
Asymptotic stability against Oleinik's monotone solutions
Use of invariant set (1.11) in Crocco transformation
Abstract
By establishing an invariant set (1.11) for the Prandtl equation in Crocco transformation, we prove orbital and asymptotic stability of Blasius-like steady states against Oleinik's monotone solutions.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Nonlinear Waves and Solitons · Molecular spectroscopy and chirality