2018/12/10 by Iyer, Sameer · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1812.03906
We characterize the well known self-similar Blasius profiles, [u, v], as downstream attractors to solutions [u,v] to the 2D, stationary Prandtl system. It was established in \citeSerrin that ‖ u - u‖L^∞y → 0 as x → ∞. Our result furthers \citeSerrin 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, Ω, 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 - u and v - v at the essentially the sharpest expected rates in Wk,p norms.