Asymptotic solutions of linearized Navier–Stokes equations localized in small neighborhoods of curves and surfaces
Anna Ivanovna Allilueva, А. И. Шафаревич · Russian Journal of Mathematical Physics · 2015
In the paper, the asymptotic behavior of solutions of the Cauchy problem is described for the linearized Navier–Stokes equation with the initial condition localized in a neighborhood of a curve or a two-dimensional surface in three-dimensional space. In particular, conditions for the growth of the perturbation in plane-parallel, two-dimensional, and helical external flows are obtained.