Asymptotic structure of the interaction in a laminar axisymmetric wake
The method of matched asymptotic expansions is used to investigate the interaction of the axisymmetric wake behind a slender body in an exterior irrotational flow in an incompressible fluid. It is shown that under certain conditions a three-layer scheme applies for the description of the flow, the perturbations of the flow in the leading approximation satisfying the Korteweg-de Vries equation. The well-known solutions of this equation in the form of a solitary wave and a cnoidal wave are considered. Also obtained are the equations of the higher approximations of the asymptotic sequence.
Abstract In this paper, we study the long-time behavior of solutions for a non-autonomous strongly damped wave equation. We first prove the existence of a uniform attractor for the equation with a translation compact driving force and then obtain an upper estimate for the Kolmogorov e -entropy of the uniform attractor. Finally we obtain an upper bound of the fractal dimension of the uniform attractor with quasiperiodic force.