Geodesic
Global solvability of a problem on two fluid motion
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 19-39

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

Unsteady motion of viscous incompressible fluids is considered in a bounded domain. The liquids are separated by an unknown interface on which the surface tension is neglected. This motion is governed by an interface problem for the Navier–Stokes system. First, a local existence theorem is established for the problem in Hölder classes of functions. The proof is based on the solvability of a model problem for the Stokes system with a plane interface which was obtained earlier. Next, for a small initial velocity vector field and small mass forces, we prove the existence of a unique smooth solution to the problem on the infinite time interval. 
@article{ZNSL_2007_348_a1,
     author = {I. V. Denisova},
     title = {Global solvability of a problem on two fluid motion},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {19--39},
     publisher = {mathdoc},
     volume = {348},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a1/}
}
TY  - JOUR
AU  - I. V. Denisova
TI  - Global solvability of a problem on two fluid motion
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2007
SP  - 19
EP  - 39
VL  - 348
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a1/
LA  - en
ID  - ZNSL_2007_348_a1
ER  - 
%0 Journal Article
%A I. V. Denisova
%T Global solvability of a problem on two fluid motion
%J Zapiski Nauchnykh Seminarov POMI
%D 2007
%P 19-39
%V 348
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a1/
%G en
%F ZNSL_2007_348_a1
I. V. Denisova. Global solvability of a problem on two fluid motion. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 19-39. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a1/