On a new class of generalized solutions for the Stokes equations in exterior domains
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 155-181. 
@article{ASNSP_1992_4_19_2_155_0,
     author = {Kozono, Hideo and Sohr, Hermann},
     title = {On a new class of generalized solutions for the {Stokes} equations in exterior domains},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {155--181},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {2},
     year = {1992},
     mrnumber = {1197210},
     zbl = {0770.35055},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1992_4_19_2_155_0/}
}
TY  - JOUR
AU  - Kozono, Hideo
AU  - Sohr, Hermann
TI  - On a new class of generalized solutions for the Stokes equations in exterior domains
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1992
SP  - 155
EP  - 181
VL  - 19
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1992_4_19_2_155_0/
LA  - en
ID  - ASNSP_1992_4_19_2_155_0
ER  - 
%0 Journal Article
%A Kozono, Hideo
%A Sohr, Hermann
%T On a new class of generalized solutions for the Stokes equations in exterior domains
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1992
%P 155-181
%V 19
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1992_4_19_2_155_0/
%G en
%F ASNSP_1992_4_19_2_155_0
Kozono, Hideo; Sohr, Hermann. On a new class of generalized solutions for the Stokes equations in exterior domains. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 155-181. http://www.numdam.org/item/ASNSP_1992_4_19_2_155_0/

[1] R.A. Adams, Sobolev spaces, New York-San Francisco -London, Academic Press 1977. | MR | Zbl

[2] N. Aronszajn - E. Gagliardo, Interpolation spaces and interpolation methods, Ann. Mat. Pura Appl. 68, 51-117 (1965). | MR | Zbl

[3] G.K. Batchelor, An Introduction to Fluid Dynamics, Cambridge, University Press 1970. | MR | Zbl

[4] J. Bergh - J. Löfström, Interpolation spaces, Berlin-Heidelberg -New York, Springer 1976. | MR | Zbl

[5] M.E. Bogovskii, Solution of the first boundary value problem for the equation of continuity of an incompressible medium, Soviet Math. Dokl. 20, 1094-1098 (1979). | MR | Zbl

[6] M.E. Bogovskii, Solution of some vector analysis problems connected with operators div and grad (in Russian). Trudy Seminar S.L. Sobolev, No. 1, 80, Sibirsk. Mat. Zh., 5-40 (1980). | MR | Zbl

[7] W. Borchers - T. Miyakawa, Algebraic L2-decay for Navier-Stokes flows in exterior domains, Acta Math. 165, 189-227 (1990). | MR | Zbl

[8] W. Borchers - H. Sohr, On the semi-group of the Stokes operator for exterior domains in Lq-spaces, Math. Z. 196, 415-425 (1987). | MR | Zbl

[9] W. Borchers - H. Sohr, On the equations rot v = g and div u = f with zero boundary conditions, Hokkaido Math. J. 19, 67-87 (1990). | MR | Zbl

[10] L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova 31, 308-340 (1961). | Numdam | MR | Zbl

[11] I.D. Chang - R. Finn, On the solutions of a class of equations occurring in continuum mechanics with application to the Stokes paradox, Arch. Rational Mech. Anal. 7, 388-401 (1961). | MR | Zbl

[12] A. Einstein, Eine neue Bestimmung der Moleküldimension, Ann. Physik 19, 289-307 (1906). | JFM

[13] R. Finn - D.R. Smith, On the linearized hydrodynamical equation in two-dimensions, Arch. Rational Mech. Anal. 25, 1-25 (1967). | MR | Zbl

[14] R. Finn, Mathematical questions relating to viscous fluid flow in an exterior domain, Rocky Mountain J. Math. 3, 107-140 (1973). | MR | Zbl

[15] A. Friedman, Partial differential equations, New York: Holt Rinehart & Winston 1969. | MR | Zbl

[16] H. Fujita, On the existence and regularity of steady state solutions of the Navier-Stokes equations, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 9, 59-102 (1961). | MR | Zbl

[17] G. Galdi - P. Maremonti, Monotonic decreasing and asymptotic behaviour of kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal. 94, 254-266 (1986). | MR | Zbl

[18] G. Galdi - C.G. Simader, Existence, uniqueness and Lq-estimates for the Stokes problem in an exterior domain, Arch. Rational Mech. Anal. 112, 291-318 (1990). | MR | Zbl

[19] Y. Giga - H. Sohr, On the Stokes operator in exterior domains, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 36, 103-130 (1989). | MR

[20] J.G. Heywood, On some paradox concerning two-dimensional Stokes flow past an obstacle, Indiana Univ. Math. J. 24, 443-450 (1974). | MR | Zbl

[21] J.G. Heywood, On uniqueness questions in the theory of viscous flow, Acta Math. 136, 61-102 (1976). | MR | Zbl

[22] H. Kozono - H. Sohr, New a priori estimates for the Stokes equations in exterior domains, Indiana Univ. Math. J. 41, 1-27 (1991). | MR | Zbl

[23] L.D. Landau - E.M. Lifschitz, Fluid Mechanics, Course of Theoretical Physics, Oxford, Pergamon Press 1987. | MR | Zbl

[24] J.L. Lions - E. Magenes, Non-homogeneous boundary value problems and applications I, Berlin-Heidelberg-New York, Springer 1972. | Zbl

[25] V.N. Maslennikova - M.A. Timoshin, On the Lp-theory for the Stokes problem in unbounded domains with compact boundary, Soviet Math. Dokl. 42, 197-201 (1991). | MR | Zbl

[26] T. Miyakawa, On nonstationary solutions of the Navier-Stokes equations in exterior domains, Hiroshima Math. J. 12, 115-140 (1982). | MR | Zbl

[27] M. Reed - B. Simon, Method of Modem Mathematical Physics II. New York- San Francisco-London, Academic Press 1975. | MR | Zbl

[28] C.G. Simader, Private communication, 1988.

[29] C.G. Simader - H. Sohr, A new approach to the Helmholtz decomposition in Lq-spaces for bounded and exterior domains, to appear in " Mathematical Problems Relating to the Navier-Stokes Equations", series on Advanced in Mathematics for Applied Sciences, vol. 11, World Scientific, 1992. | MR | Zbl

[30] H. Sohr - W. Varnhorn, On decay properties of the Stokes equations in exterior domains, Lecture Notes in Math. no. 1431 Heywood, J.G., et al. eds., Proceedings, Obelwolfach 1988, Berlin-Heidelberg- New York, Springer 134-151 (1990). | MR | Zbl

[31] R. Temam, Navier-Stokes equations, Amsterdam, North-Holland 1977. | MR | Zbl

[32] H. Triebel, Interpolation theory, function spaces, differential operators, Amsterdam, North-Holland 1978. | MR | Zbl

[33] K. Yosida, Functional analysis, Berlin-Heidelberg -New York, Springer 1965. | Zbl