The strong solvability of the nonstationary Stokes problem with nonzero divergence in a bounded domain is studied. Bibliography: 12 titles.
Similar content being viewed by others
References
O. V. Besov, V. P. Il’in, and S. M. Nikolskii, Integral Representations of Functions and Imbedding Theorems [in Russian], Nauka, Moscow (1975).
M. E. Bogovskii, “On solution of some problems of vectoral analysis related to div and grad operators,” in: Proceedings of the S. L. Sobolev Seminar, 1 (1980), pp. 5-40.
L. Caffarelli, R. V. Kohn, and L. Nirenberg, “Partial regularity of suitable weak solutions of the Navier-Stokes equations,” Comm. Pure Appl. Math., 35, 771-831 (1982).
R. Farwig and H. Sohr, “The stationary and nonstationary Stokes system in exterior doamains with nonzero divergence and nonzero boundery data,” Math. Meth. Appl. Sci., 17, 269-291 (1994).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, Rhode Island (1967).
G. A. Seregin, “Some estimates near the boundary for solutions to the nonstationary linearized Navier-Stokes equations,” Zap. Nauchn. Semin. POMI, 271, 204-223 (2000).
G. A. Seregin, “Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary,” J. Math. Fluid Mech., 4, no. 1, 1-29 (2002).
G. A. Seregin, “Local regularity theory of the Navier-Stokes equations,” in: Handbook of Mathematical Fluid Dynamics, Vol. 4 (2007), pp. 159-200.
V. A. Solonnikov, “Estimates in L p of solutions to the initial-boundary value problem for the generalized Stokes system in a bounded domain,” Probl. Math. Anal., 21, 211-263 (2000).
V. A. Solonnikov, “Estimates of solutions of the Stokes equations in Sobolev spaces with a mixed norm,” Zap. Nauchn. Semin POMI, 288, 204-231 (2002).
V. A. Solonnikov, “On the estimates of solutions of nonstationary Stokes problem in anisotropic Sobolev spaces and on the estimate of resolvent of the Stokes problem,” Usp. Mat. Nauk, 58, no. 2 (350), 123-156 (2003).
D. K. Faddeev, B. Z. Vulich, V. A. Solonnikov, and N. N. Uraltseva, Selected Chapters in Analysis and Higher Algebra [in Russian], LGU (1981).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 370, 2009, pp. 184–202.
Rights and permissions
About this article
Cite this article
Filinov, N., Shilkin, T. On the Stokes problem with nonzero divergence. J Math Sci 166, 106–117 (2010). https://doi.org/10.1007/s10958-010-9849-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-9849-5