DOI: 10.1007/bf00276188. On the Navier-Stokes initial value problem. I

On the Navier-Stokes initial value problem. I

10.1007/bf00276188

Crossref journal-article

Springer Science and Business Media LLC

Archive for Rational Mechanics and Analysis (297)

Bibliography

Fujita, H., & Kato, T. (1964). On the Navier-Stokes initial value problem. I. Archive for Rational Mechanics and Analysis, 16(4), 269â315.

Authors 2

Hiroshi Fujita (first)
Tosio Kato (additional)

References 24 Referenced 906

Cattabriga, L., Su un problema al contorno relativo al sistema di equazioni di Stokes. Rendiconti Seminario Mat. Univ. Padova, 31, 1?33 (1961). / Rendiconti Seminario Mat. Univ. Padova by L. Cattabriga (1961)
Golovkin, K. K., & B. A. Solonnikov, On the first boundary value problem for the non-stationary Navier-Stokes equation. Doklady Akad. Nauk USSR 140, 287?290 (1961). / Doklady Akad. Nauk USSR by K. K. Golovkin (1961)
Fujita, H., On the existence and regularity of the steady-state solutions of the Navier-Stokes equation. J. Fac. Sci., Univ. Tokyo, Sec. I 9, 59?102 (1961). / J. Fac. Sci., Univ. Tokyo, Sec. I by H. Fujita (1961)
Fujita, H., Unique existence of solutions of the Navier-Stokes initial value problem, (an application of fractional powers of operators). Sûgaku (Iwanami) 14, 65?81 (1962). / Sûgaku (Iwanami) by H. Fujita (1962)
Hopf, E., Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4, 213?231 (1951). (10.1002/mana.3210040121) / Math. Nachr. by E. Hopf (1951)
Ito, S., The existence and the uniqueness of regular solution of non-stationary Navier-Stokes equation. J. Fac. Sci., Univ. Tokyo, Sec. I 9, 103?140 (1961). / J. Fac. Sci., Univ. Tokyo, Sec. I by S. Ito (1961)
Kato, T., Abstract evolution equation of parabolic type in Banach and Hilbert spaces. Nagoya Math. J. 19, 93?125 (1961). (10.1017/S0027763000002415) / Nagoya Math. J. by T. Kato (1961)
Kato, T., Fractional powers of dissipative operators. J. Math. Soc. Japan 13, 246?274 (1961). (10.2969/jmsj/01330246) / J. Math. Soc. Japan by T. Kato (1961)
Kato, T., A generalization of the Heinz inequality. Proc. Japan Acad. 37, 305?308 (1961). (10.3792/pja/1195523678) / Proc. Japan Acad. by T. Kato (1961)
Kato, T., & H. Fujita, On the non-stationary Navier-Stokes system. Rendiconti Seminario Math. Univ. Padova 32, 243?260 (1962). / Rendiconti Seminario Math. Univ. Padova by T. Kato (1962)
Kiselev, A. A., & O. A. Ladyzhenskaia, On existence and uniqueness of the solution of the non-stationary problem for any incompressible viscous fluid. Izv. Akad. Nauk. USSR, 21, 655?680 (1957). / Izv. Akad. Nauk. USSR by A. A. Kiselev (1957)
Ladyzhenskaia, O. A., Solution ?in the large? of the non-stationary boundary value problem for the Navier-Stokes system with two space variables. Comm. Pure Appl. Math. 12, 427?433 (1959). (10.1002/cpa.3160120303) / Comm. Pure Appl. Math. by O. A. Ladyzhenskaia (1959)
Ladyzhenskaia, O. A., Mathematical Problems for Dynamics of Viscous Incompressible Fluids. Moscow 1961.
Leray, J., Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique. J. Math. Pures Appl., Ser. IX 12 1?82 (1933). / J. Math. Pures Appl., Ser. IX by J. Leray (1933)
Leray, J., Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193?248 (1934). (10.1007/BF02547354) / Acta Math. by J. Leray (1934)
Lions, J. L., Sur la régularité et l'unicité des solutions turbulentes des équations de Navier-Stokes. Rendiconti Seminario Mat. Univ. Padova 30, 16?23 (1960). / Rendiconti Seminario Mat. Univ. Padova by J. L. Lions (1960)
Lions, J. L., Sur les espaces d'interpolation; dualité. Math. Scand. 9, 147?177 (1961). (10.7146/math.scand.a-10632) / Math. Scand. by J. L. Lions (1961)
Lions, J. L., & G. Prodi, Un théorème d'existence et unicité dans les équations de Navier-Stokes en dimension 2. C.R. Acad. Sci. Paris 248, 3519?3521 (1959). / C.R. Acad. Sci. Paris by J. L. Lions (1959)
Odqvist, F. K. G., Über die Randwertaufgabe der Hydrodynamik zäher Flüssigkeiten. Math. Z. 32, 329?375 (1930). (10.1007/BF01194638) / Math. Z. by F. K. G. Odqvist (1930)
Ohyama, T., Interior regularity of weak solutions of the time-dependent Navier Stokes equation. Proc. Japan Acad. 36, 273?277 (1960). (10.3792/pja/1195524029) / Proc. Japan Acad. by T. Ohyama (1960)
Oseen, C. W., Hydrodynamik. Leipzig 1927.
Serrin, J., On the interior regularity of weak solutions of the Navier-Stokes equation. Arch. Rational Mech. Anal. 9, 187?195 (1962). (10.1007/BF00253344) / Arch. Rational Mech. Anal. by J. Serrin (1962)
Sobolevskii, P. E., On non-stationary equations of hydrodynamics for viscous fluid. Doklady Akad. Nauk USSR 128, 45?18 (1959). / Doklady Akad. Nauk USSR by P. E. Sobolevskii (1959)
Sobolevskii, P. E., On the smoothness of generalized solutions of the Navier-Stokes equation, ibid Nauk USSR 131, 758?760 (1960).

Dates

Type	When
Created	20 years, 10 months ago (Oct. 2, 2004, 9:12 p.m.)
Deposited	6 years, 4 months ago (April 3, 2019, 10:26 a.m.)
Indexed	17 minutes ago (Aug. 28, 2025, 3:19 a.m.)
Issued	61 years, 7 months ago (Jan. 1, 1964)
Published	61 years, 7 months ago (Jan. 1, 1964)
Published Print	61 years, 7 months ago (Jan. 1, 1964)

Funders 0

None

BibTeX

@article{Fujita_1964, title={On the Navier-Stokes initial value problem. I}, volume={16}, ISSN={1432-0673}, url={http://dx.doi.org/10.1007/bf00276188}, DOI={10.1007/bf00276188}, number={4}, journal={Archive for Rational Mechanics and Analysis}, publisher={Springer Science and Business Media LLC}, author={Fujita, Hiroshi and Kato, Tosio}, year={1964}, pages={269–315} }

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