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 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 
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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

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