Geodesic
Global solutions of the~Navier--Stokes equations in a~uniformly rotating space
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 196-215

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the Cauchy problem for the Navier–Stokes system of equations in a three-dimensional space rotating uniformly about the vertical axis with the periodicity condition with respect to the spatial variables. Studying this problem is based on expanding given and sought vector functions in Fourier series in terms of the eigenfunctions of the curl and Stokes operators. Using the Galerkin method, we reduce the problem to the Cauchy problem for the system of ordinary differential equations, which has a simple explicit form in the basis under consideration. Its linear part is diagonal, which allows writing explicit solutions of the linear Stokes–Sobolev system, to which fluid flows with a nonzero vorticity correspond. Based on the study of the nonlinear interaction of vortical flows, we find an approach that we can use to obtain families of explicit global solutions of the nonlinear problem.
Keywords: eigenfunction, eigenvalue, curl operator, Stokes operator, Navier–Stokes system of equations, Fourier method, Galerkin method. 
@article{TMF_2010_162_2_a2,
     author = {R. S. Saks},
     title = {Global solutions of {the~Navier--Stokes} equations in a~uniformly rotating space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {196--215},
     publisher = {mathdoc},
     volume = {162},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a2/}
}
TY  - JOUR
AU  - R. S. Saks
TI  - Global solutions of the~Navier--Stokes equations in a~uniformly rotating space
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 196
EP  - 215
VL  - 162
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a2/
LA  - ru
ID  - TMF_2010_162_2_a2
ER  - 
%0 Journal Article
%A R. S. Saks
%T Global solutions of the~Navier--Stokes equations in a~uniformly rotating space
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 196-215
%V 162
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a2/
%G ru
%F TMF_2010_162_2_a2
R. S. Saks. Global solutions of the~Navier--Stokes equations in a~uniformly rotating space. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 2, pp. 196-215. http://geodesic.mathdoc.fr/item/TMF_2010_162_2_a2/