- Tytuł:
- On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion
- Autorzy:
-
Mucha, Piotr
Zajączkowski, Wojciech - Powiązania:
- https://bibliotekanauki.pl/articles/1208168.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
anisotropic Sobolev space
Navier-Stokes equations
local existence
sharp regularity
incompressible viscous barotropic self-gravitating fluid - Opis:
- 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.
- Źródło:
-
Applicationes Mathematicae; 2000, 27, 3; 319-333
1233-7234 - Pojawia się w:
- Applicationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł