Geodesic
On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 319-333.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The local-in-time existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion is proved. We show the existence of solutions with lowest possible regularity for this problem such that $u\in W^{2,1}_r(\widetilde{{\mitΩ}}^T)$ with r>3. The existence is proved by the method of successive approximations where the solvability of the Cauchy-Neumann problem for the Stokes system is applied. We have to underline that in the $L_p$-approach the Lagrangian coordinates must be used. We are looking for solutions with lowest possible regularity because this simplifies the proof and decreases the number of compatibility conditions.
DOI : 10.4064/am-27-3-319-333
Keywords: anisotropic Sobolev space, Navier-Stokes equations, local existence, sharp regularity, incompressible viscous barotropic self-gravitating fluid

Piotr Mucha 1 ; Wojciech Zajączkowski 1

1 
@article{10_4064_am_27_3_319_333,
     author = {Piotr Mucha and Wojciech Zaj\k{a}czkowski},
     title = {On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion},
     journal = {Applicationes Mathematicae},
     pages = {319--333},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2000},
     doi = {10.4064/am-27-3-319-333},
     zbl = {0996.35050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-319-333/}
}
TY  - JOUR
AU  - Piotr Mucha
AU  - Wojciech Zajączkowski
TI  - On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
JO  - Applicationes Mathematicae
PY  - 2000
SP  - 319
EP  - 333
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-319-333/
DO  - 10.4064/am-27-3-319-333
LA  - en
ID  - 10_4064_am_27_3_319_333
ER  - 
%0 Journal Article
%A Piotr Mucha
%A Wojciech Zajączkowski
%T On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
%J Applicationes Mathematicae
%D 2000
%P 319-333
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-319-333/
%R 10.4064/am-27-3-319-333
%G en
%F 10_4064_am_27_3_319_333
Piotr Mucha; Wojciech Zajączkowski. On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion. Applicationes Mathematicae, Tome 27 (2000) no. 3, pp. 319-333. doi : 10.4064/am-27-3-319-333. http://geodesic.mathdoc.fr/articles/10.4064/am-27-3-319-333/

Cité par Sources :