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References
Calderon, A. P., & A. Zygmund, On the existence of certain singular integrals. Acta Math. 88, 85–139 (1952).
Hopf, Eberhard, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachrichten 4 (1951).
Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach 1969.
Leray, J., Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193–248 (1934).
Lewis, J. E., Mixed estimates for singular integrals, Proceedings of Symposia in Pure Mathematics. A.M.S., Vol. X.
Lions, J. L., Quelques méthodes de resolution des problèmes aux limites non linéaires. Paris: Dunod, Gauthier-Villars 1969.
Oseen, C. W., Neuere Methoden und Ergebnisse in der Hydrodynamik, p. 68. Leipzig: Akademische Verlagsgesellschaft m.b.h. 1927.
Prodi, G., Un teorema di unicitá per le equazioni di Navier-Stokes. Annali di Mat. 48, 173–182 (1959).
Riviere, N. M., Singular integrals and multiplier operators, Arkiv för Math. (to appear).
Serrin, J., The Initial Value Problem for the Navier-Stokes Equations. Nonlinear Problems, edited by R. E. Langer, University of Wisconsin press, 1963, 69–83.
Stein, E. M., Singular Integrals and Differentiability Properties of Functions. Princeton Univ. Press 1970.
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Comminicated by J. Serrin
We wish to thank Professors L. Hörmander and G. Knightly for their valuable comments.
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Fabes, E.B., Jones, B.F. & Riviere, N.M. The initial value problem for the Navier-Stokes equations with data in Lp . Arch. Rational Mech. Anal. 45, 222–240 (1972). https://doi.org/10.1007/BF00281533
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DOI: https://doi.org/10.1007/BF00281533