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Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes. (German) Zbl 0506.35084

MSC:
35Q30 Navier-Stokes equations
35D10 Regularity of generalized solutions of PDE (MSC2000)
35B45 A priori estimates in context of PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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References:
[1] Adams, R.A.: Sobolev Spaces. New York-San Francisco-London: Academic Press 1975 · Zbl 0314.46030
[2] Bemelmans, J.: Eine Außenraumaufgabe für die instationären Navier-Stokes-Gleichungen. Math. Z.162, 145-173 (1978) · Zbl 0379.35053 · doi:10.1007/BF01215072
[3] Gerhardt, C.: Stationary Solutions to the Navier-Stokes Equations in Dimension Four. Math. Z.165, 193-197 (1979) · Zbl 0405.35064 · doi:10.1007/BF01182469
[4] Giga, Y.: Analyticity of the Semigroup Generated by the Stokes Operator inL r Spaces. Math. Z.178, 297-329 (1981) · Zbl 0461.47019 · doi:10.1007/BF01214869
[5] Giga, Y.: The Stokes Operator inL r Spaces. Proc. Japan Acad. Ser. A Math. Sci.57, 85-89 (1981) · Zbl 0471.35069 · doi:10.3792/pjaa.57.85
[6] Fabes, E.B., Jones, B.F., Riviere, N.M.: The Initial Value Problem for the Navier-Stokes Equations with Data inL p Arch. Rational Mech. Anal.45, 222-240 (1972) · Zbl 0254.35097 · doi:10.1007/BF00281533
[7] Fujiwara, D., Morimoto, H.: AnL r -theorem of Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math.24, 685-700 (1977) · Zbl 0386.35038
[8] Heywood, J.G., The Navier Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J.29, 639-681 (1980) · Zbl 0494.35077 · doi:10.1512/iumj.1980.29.29048
[9] Heywood, J.G., Rannacher, R.: Finite Element Approximation of the Nonstationary Navier-Stokes Problem. SIAM J. Numer. Anal.19, 275-311 (1982) · Zbl 0487.76035 · doi:10.1137/0719018
[10] Hopf, E.: Über die Anfangswertaufgaben für die hydrodynamischen Gleichungen. Math. Nachr.4, 213-231 (1951) · Zbl 0042.10604
[11] Krasnoselski, M.A.: Integral operators in spaces of summable functions. Leyden: Noordhoff International Publishing 1976
[12] Masuda, K.: On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan27, 294-327 (1975) · Zbl 0303.76011 · doi:10.2969/jmsj/02720294
[13] Miyakawa, T.: On the initial value problem for the Navier-Stokes equation inL p -spaces. Hiroshima Math. J.118, 9-20 (1981) · Zbl 0457.35073
[14] Miyakawa, T.: On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J.12, 115-140 (1982) · Zbl 0486.35067
[15] Ne?as, J.: Les méthodes directes en theorie des équations elliptiques. Prague: Éditeurs Academia 1967
[16] Seeley, R.: Norms and Domains of the Complex PowersA B z Amer. J. Math.93, 299-309 (1971) · Zbl 0218.35034 · doi:10.2307/2373377
[17] Serrin, J.: The initial value problem for the Navier-Stokes equations. Nonlinear Problems, Proceedings of a Symposium (Madison 1962) pp. 69-98. Madison, Wisconsin: Univ. of Wisconsin Press 1963
[18] Serrin, J.: On the Interior Regularity of Weak Solutions of the Navier-Stokes Equations. Arch. Rational Mech. Anal.9, 187-195 (1962) · Zbl 0106.18302 · doi:10.1007/BF00253344
[19] Sobolevski, P.E.: Study of Navier-Stokes equations by the methods of the theory of parabolic equations in Banach spaces. Soviet Math. Dokl.5, 720-723 (1964)
[20] Solonnikov, V.A.: Estimates for solutions of nonstationary Navier-Stokes equations. J. Soviet Math.8, 467-529 (1977) · Zbl 0404.35081 · doi:10.1007/BF01084616
[21] Solonnikov, V.A.: Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations. Amer. Math. Soc. Transl.75, 1-116 (1968) · Zbl 0187.03402
[22] Specovius, M.: Über einen Struktursatz von Leray für Lösungen Navier-Stokesscher Anfangswertaufgaben. Diplomarbeit, Universität-Gesamthochschule Paderborn 1981
[23] Temam, R.: Navier-Stokes Equations. Amsterdam-New York-Oxford: North-Holland 1977 · Zbl 0383.35057
[24] Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators. Amsterdam-New York-Oxford: North-Holland 1978 · Zbl 0387.46032
[25] Wahl, W. von: Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen. J. Math. Soc. Japan,32, 263-283 (1980) · Zbl 0456.35073 · doi:10.2969/jmsj/03220263
[26] Wahl, W. von: Nichtlineare Evolutionsgleichungen. Teubner-Texte zur Math.50, pp. 294-302. Leipzig: Teubner 1983
[27] Walter, W.: Gewöhnliche Differentialgleichungen. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0327.34001
[28] Yosida, K.: Functional Analysis. Grundlehren Math. Wiss.123. Berlin-Heidelberg-New York: Springer 1965 · Zbl 0126.11504
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