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References
Cattabriga, L., Su un problema al contorno relativo al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova 31, 308–340 (1961).
Fujita, H., & T. Kato, On the Navier-Stokes initial value problem I. Arch. Rational Mech. Anal. 46, 269–315 (1964).
Fujita, H., & H. Morimoto, On fractional powers of the Stokes operator. Proc. Japan Acad. 16, 1141–1143 (1970).
Fujiwara, D., On the asymptotic behaviour of the Green operators for elliptic boundary problems and the pure imaginary powers of some second order operators. J. Math. Soc. Japan 21, 481–521 (1969).
Fujiwara, D., & H. Morimoto, An Lr-theorem of the Helmholtz decomposition of vector fields. J. Fac. Sci. Univ. Tokyo Sec. I 24, 685–700 (1977).
Giga, Y., Analyticity of the semigroup generated by the Stokes operator in L r spaces. Math. Z. 178, 297–329 (1981).
Giga, Y., The Stokes operator in L r spaces. Proc. Japan Acad. 57, 85–89 (1981).
Giga, Y., & T. Miyakawa, Solutions in L r to the Navier-Stokes initial value problem. Arch. Rational Mech. Anal. 89, 267–281 (1985).
Kato, T., Fractional powers of dissipative operators II. J. Math. Soc. Japan 14, 242–248 (1962).
Kato, T., & H. Fujita, On the nonstationary Navier-Stokes system. Rend. Sem. Mat. Univ. Padova 32, 243–260 (1962).
Kumano-go, H., Pseudo-differential operators. Tokyo: Iwanami 1974 (in Japanese).
Kumano-go, H., & M. Nagase, Lp-theory of pseudo-differential operators. Proc. Japan Acad. 46, 138–142 (1970).
Ladyzhenskaya, O. A., The mathematical theory of viscous incompressible flow. New York: Gordon and Breach 1969.
Miyakawa, T., On the initial value problem for the Navier-Stokes equations in L p spaces. Hiroshima Math. J. 11, 9–20 (1981).
Seeley, R., Norms and domains of the complex powers A. Amer. J. Math. 93, 299–300 (1971).
Sobolevskii, P. E., The use of fractional powers of operators in studying the NavierStokes equations. Soviet Math. Dokl. 5, 356–359 (1964).
Sobolevskii, 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).
Solonnikov, V. A., Estimates for solutions of nonstationary Navier-Stokes equations. J. Soviet Math. 8, 467–529 (1977).
Wahl, W. Von, Regularity questions for the Navier-Stokes equations. Lecture Note in Math. 771, pp. 538–542. Berlin Heidelberg New York: Springer 1980.
Wahl, W. Von, A book to be published.
Weissler, F. B., The Navier-Stokes initial value problem in L p. Arch. Rational Mech. Anal. 74, 219–230 (1980).
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Giga, Y. Domains of fractional powers of the Stokes operator in Lr spaces. Arch. Rational Mech. Anal. 89, 251–265 (1985). https://doi.org/10.1007/BF00276874
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DOI: https://doi.org/10.1007/BF00276874