Abstract
The paper contains estimates of the volume and surface potentials arising in the evolution free boundary problem for a viscous self-gravitating liquid. The densities and domain where the potentials are defined may depend on time. The estimates are obtained in weighted anisotropic Sobolev-Slobodetskii spaces. Bibliography: 4 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. A. Solonnikov, “On the stability of uniformly rotating viscous incompressible self-gravitating liquid” J. Math. Sci., New York 152 (2008), no. 5, 4343–4370.
V. A. Solonnikov, On the Non-Stationary Motion of a Viscous Incompressible Liquid over a Rotating Ball, Preprint, POMI (2008).
Y. Hataya, “Decaying solutions of the Navier-Stokes flow without surface tension,” J. Math. Kyoto Univ. [Submitted]
V. A. Solonnikov, “On the estimates of the volume and surface potentials in domains with boundaries of class W 2l ” [in Russian], Probl. Mat. Anal. 36 (2008), 93–111; English transl.: J. Math. Sci., New York 150 (2008), no. 1, 1893–1919.
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Problemy Matematicheskogo Analiza, No. 37, 2008, pp. 83–117.
Rights and permissions
About this article
Cite this article
Solonnikov, V.A. On estimates for potentials related to the problem of stability of a rotating self-gravitating liquid. J Math Sci 154, 90–124 (2008). https://doi.org/10.1007/s10958-008-9155-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-008-9155-7