Bulletin of the American Mathematical Society

MathSciNet review: 1567693
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Book Information:

Author: Wolf von Wahl
Title: The equations of Navier-Stokes and abstract parabolic equations
Additional book information: Friedr. Vieweg & Sohn, Braunschweig and Wiesbaden, xxiv + 264 pp. (paperback). ISBN 3-528-08915-6.

Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269–315. MR 166499, DOI 10.1007/BF00276188

Yoshikazu Giga, Analyticity of the semigroup generated by the Stokes operator in $L_{r}$ spaces, Math. Z. 178 (1981), no. 3, 297–329. MR 635201, DOI 10.1007/BF01214869

Yoshikazu Giga, Domains of fractional powers of the Stokes operator in $L_r$ spaces, Arch. Rational Mech. Anal. 89 (1985), no. 3, 251–265. MR 786549, DOI 10.1007/BF00276874

Eberhard Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr. 4 (1951), 213–231 (German). MR 50423, DOI 10.1002/mana.3210040121

Tosio Kato and Hiroshi Fujita, On the nonstationary Navier-Stokes system, Rend. Sem. Mat. Univ. Padova 32 (1962), 243–260. MR 142928

Jean Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math. 63 (1934), no. 1, 193–248 (French). MR 1555394, DOI 10.1007/BF02547354

James Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 9 (1962), 187–195. MR 136885, DOI 10.1007/BF00253344

James Serrin, The initial value problem for the Navier-Stokes equations, Nonlinear Problems (Proc. Sympos., Madison, Wis., 1962) Univ. Wisconsin Press, Madison, Wis., 1963, pp. 69–98. MR 0150444

P. E. Sobolevskiĭ, Non-stationary equations of viscous fluid dynamics, Dokl. Akad. Nauk SSSR 128 (1959), 45–48 (Russian). MR 0110895

V. A. Solonnikov, Estimates of the solutions of the nonstationary Navier-Stokes system, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 38 (1973), 153–231 (Russian). Boundary value problems of mathematical physics and related questions in the theory of functions, 7. MR 0415097

Roger Temam, Navier-Stokes equations. Theory and numerical analysis, Studies in Mathematics and its Applications, Vol. 2, North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. MR 0609732

H. Fujita and T. Kato (1964), On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16, 269-315. MR 0166499




Y. Giga (1981), Analyticity of the semigroup generated by the Stokes operator in L, Math. Z. 178, 297-329. MR 635201




Y. Giga (1985), Domains of fractional powers of the Stokes operator in L, Arch. Rational Mech. Anal. 89, 251-265. MR 786549




E. Hopf (1951), Über die Anfangwertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nach. 4, 213-231. MR 50423




T. Kato and H. Fujita (1962), On the nonstationary Navier-Stokes system, Rend. Sem. Math. Univ. Padova 32, 243-260. MR 142928




J. Leray (1934), Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63, 193-248. MR 1555394




J. Serrin (1962), On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 9, 187-195. MR 136885




J. Serrin (1963), The initial value problem for the Navier-Stokes equations, Nonlinear Problems (R. E. Langer, ed.), pp. 69-98, Univ. of Wisconsin Press, Madison. MR 150444




P. E. Sobolevskiĭ (1959), On non-stationary equations of hydrodynamics for viscous fluid, Dokl. Akad. Nauk SSSR 128, 45-48 (Russian). MR 110895




V. A. Solonnikov (1973), Estimates for solutions of nonstationary Navier-Stokes equations, J. Soviet Math. 8 (1977), 467-529; original in Zapiski Nauchn. Sem. LOMI im. V. A. Steklova AN SSSR 38, 153-231. MR 415097




R. Temam (1977), Navier-Stokes equations, North-Holland, Amsterdam. MR 609732