@article{ASNSP_1997_4_24_3_395_0, author = {Maremonti, P. and Solonnikov, V. A.}, title = {On nonstationary {Stokes} problem in exterior domains}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {395--449}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 24}, number = {3}, year = {1997}, mrnumber = {1612381}, zbl = {0958.35103}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1997_4_24_3_395_0/} }
TY - JOUR AU - Maremonti, P. AU - Solonnikov, V. A. TI - On nonstationary Stokes problem in exterior domains JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1997 SP - 395 EP - 449 VL - 24 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1997_4_24_3_395_0/ LA - en ID - ASNSP_1997_4_24_3_395_0 ER -
%0 Journal Article %A Maremonti, P. %A Solonnikov, V. A. %T On nonstationary Stokes problem in exterior domains %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1997 %P 395-449 %V 24 %N 3 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1997_4_24_3_395_0/ %G en %F ASNSP_1997_4_24_3_395_0
Maremonti, P.; Solonnikov, V. A. On nonstationary Stokes problem in exterior domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 24 (1997) no. 3, pp. 395-449. http://www.numdam.org/item/ASNSP_1997_4_24_3_395_0/
[1] Convolution operators on Banach space valuedfunctions, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 356-365. | MR | Zbl
- - ,[2] Integral representations of functions and imbedding theorems, V.H. Winston & Sons,1978. | Zbl
- - ,[3] Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl. 20 (1979), 1094-1098. | MR | Zbl
,[4] Algebraic L2 decay for Navier-Stokes flows in exterior domains, Acta Math. 165 (1990), 189-227. | MR | Zbl
- ,[5] L2-decay for Navier-Stokes Flows in unbounded domains, with application to exterior stationary flows, Arch. Rational Mech. Anal. 118 (1992), 273-295. | MR | Zbl
- ,[6] On the boundedness of the Stokes semigroup in two-dimensional exterior domains, Math. Z. 213 (1993), 275-299. | MR | Zbl
- ,[7] The stationary and non-stationary Stokes system in exterior domains with non-zero divergence and non-zero boundary values, Math. Methods Appl. Sci. 17 (1994), 269-291. | MR | Zbl
- ,[8] Une remarque sur l'unicité des solutions des équations de Navier-Stokes en dimension n, Bull. Soc. Math. France 89 (1961), 1-8. | Numdam | MR | Zbl
,[9] An introduction to the Mathematical theorey of the Navier-Stokes equations, Springer-Verlag, 1994.
,[10] Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal. 94 (1986), 253-266. | MR | Zbl
- ,[11] Existence, uniqueness and Lq estimates for the Stokes problem in an exterior doamin, Arch. Rational Mech. Anal. 112 (1990), 291-318. | MR | Zbl
- ,[12] On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo 36 (1989), 103-130. | MR
- ,[13] Abstract LP estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains, J. Funct. Anal. 102 (1991), 72-94. | MR | Zbl
- ,[14] LP estimates for the Stokes system, Func. Analysis and Related Topics 102 (1991), 55-67. | MR | Zbl
- ,[15] Lq - Lr estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in Lq spaces, Math. Ann. 285 (1989), 265-288. | MR | Zbl
,[16] Decay properties of strong solutions for the Navier-Stokes equations in two-dimensional unbounded domains, Arch. Rational Mech. Anal. 122 (1993), 1-17. | MR | Zbl
- ,[17] The mathematical theory of viscous incompressible flow, Gordon and Breach, 1969. | MR | Zbl
,[18] Linear and quasilinear equations of parabolic type, Translations of Math. Monographs AMS 23, 1968. | Zbl
- - ,[19] On the asymptotic behaviour of the L2-norm of suitable weak solutions to the Navier-Stokes equations in three-dimensional exterior domains, Comm. Math. Phys. 198 (1988), 385-400. | MR | Zbl
,[20] Some results on the asymptotic behaviour of Hopf weak solutions to the Navier-Stokes equations in unbounded domains, Math. Z. 210 (1992), 1-22. | MR | Zbl
,[21] An estimate for solutions of the Stokes system in exterior domains, Zap. Nauch. Sem. LOMI 180 (1990), 105-120. | MR | Zbl
- ,[22] On the estimates of solutions of evolution Stokes problem in anisotropic Sobolev spaces with a mixed norm, Zap. Nauch. Sem. LOMI 223 (1994), 124-150. | MR | Zbl
- ,[23] Istituzioni di analisi funzionale lineare, Unione Mat. Italiana, Oderisi Gubbio Ed., 1978.
,[24] The nonstationary problem for the Navier-Stokes equations in regions with moving bounadaries, J.Math. Soc. Japan 42 (1990), 495-502. | MR | Zbl
,[25] The Helmholtz decomposition in Lq and related topics, Math. Problems Related to the Navier-Stokes Equations, Galdi G.P. Ed., Advances in Math. for Applied Sc., World Scientific 11 1992, 1-35. | MR | Zbl
- ,[26] Estimates for the solutions of a nonstationary linearized system of Navier-Stokes equations, Tran. Amer. Math. Soc. 75 (1968), 1-116. | Zbl
,[27] Estimates for solutions of nonstationary Navier-Stokes equations, J. Soviet Math. 8 (1977), 467-528. | Zbl
,[28] A-priori estimates for second order equations of parabolic type, Proceedings of Steklov Math. Inst. 70 (1964), 133-212. | MR | Zbl
,[29] A solution formula for the Stokes equation in Rn+, Comm. Pure Appl. Math. 40 (1987), 611-621. | MR | Zbl
,[30] The equations of Navier-Stokes and abstract parabolic equations, Vieweg, Braunschweig-Wiesbaden, 1985. | MR
,[31] Method of linearization in hydrodinamical stability theory, Rostov University, 1984. | Zbl
,