On local existence of solutions of the free boundary problem for an incompressible viscous self-gravitating fluid motion

Volume 27 / 2000

Piotr Mucha, Wojciech Zajączkowski Applicationes Mathematicae 27 (2000), 319-333 DOI: 10.4064/am-27-3-319-333

Abstract

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.

Authors

  • Piotr Mucha
  • Wojciech Zajączkowski

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