Solutions symétriques du problème de Leray

Результат исследования: Научные публикации в периодических изданияхстатья


A stationary boundary-value problem for the Navier–Stokes equations of an incompressible fluid in a domain of a spherical layer type is considered. The velocity vector on the boundary is given. The solvability of this problem was proven by Jean Leray (1933) under an additional condition of a zero flux through each connected component of the flow domain boundary. The following problem is open up to now: does a solution to the flux problem exist if only the necessary condition of a zero total flux is satisfied? The present communication is devoted to the consideration of the Leray problem in a spherical-layer-type domain. An a priori estimate of the solution under the condition of flow symmetry with respect to a plane is obtained. This estimate implies the solvability of the problem.

Переведенное названиеSymmetric solutions to the Leray problem
Язык оригиналафранцузский
Страницы (с-по)113-117
Число страниц5
ЖурналComptes Rendus Mathematique
Номер выпуска1
СостояниеОпубликовано - 1 янв 2017

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