Time evolution of the Navier-Stokes flow in far-field
arXiv:2302.12557 · doi:10.1007/s00021-024-00904-0
Abstract
Asymptotic expansion in far-field for the incompressive Navier-Stokes flow are established. Under moment conditions on the initial vorticity, technique of renormalization together with Biot-Savard law derives an asymptotic expansion for the velocity with high-order. Especially scalings and large-time behaviors of the expansions are clarified. By employing them, time evolution of velocity in far-field is drawn. As an appendix, asymptotic behavior of solutions as time variable tends to infinity is given.
18 pages