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- W2021073558 abstract "Communications on Pure and Applied MathematicsVolume 35, Issue 6 p. 771-831 Article Partial regularity of suitable weak solutions of the navier-stokes equations L. Caffarelli, L. CaffarelliSearch for more papers by this authorR. Kohn, R. KohnSearch for more papers by this authorL. Nirenberg, L. NirenbergSearch for more papers by this author L. Caffarelli, L. CaffarelliSearch for more papers by this authorR. Kohn, R. KohnSearch for more papers by this authorL. Nirenberg, L. NirenbergSearch for more papers by this author First published: November 1982 https://doi.org/10.1002/cpa.3160350604Citations: 919AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 Almgren, F., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. Math. 87, 1968, pp. 321– 391. 2 Caffarelli, L., Kohn, R., and Nirenberg, L., First-order interpolation inequalities with weights, in preparation. 3 Fabes, E., Lewis, J., and Rivière, N., Singular integrals and hydrodynamic potentials, Amer. J. Math. 99, 1977, pp. 601– 625. 4 Fabes, E., Lewis, J., and Rivière, N., Boundary value problems for the Navier-Stokes equations, Amer. J. Math. 99, 1977, pp. 626– 668. 5 Federer, H., Geometric Measure Theory, Springer-Verlag, New York, 1969. 6 Foias, C., and Témam, R., Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations, J. Math. Pures et Appl. 58, 1979, pp. 339– 368. 7 Fujita, H., and Kato, T., On the Navier-Stokes initial value problem I, Arch. Ration. Mech. Anal. 16, 1964, pp. 269– 315. 8 Fujiwara, D., and Morimoto, H., An Lr theorem on the Helmholtz decomposition of vector fields, Tokyo Univ. Fac. Sciences J. 24, 1977, pp. 685– 700. 9 Gagliardo, E., Ulteriori proprietà di alcune classi di funzioni in più variabili, Richerche di Mat. Napoli 8, 1959, pp. 24– 51. 10 Giga, Y., and Miyakawa, T., Solutions in Lr to the Navier-Stokes initial value problem, preprint. 11 Golovkin, K. K., and Ladyzenskaya, O. A., Solutions of non-stationary boundary value problems for the Navier-Stokes equations, Trudy Mat. Inst. Steklov 59, 1960, pp. 100– 114 (In Russian). 12 Hopf, E., Uber die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr. 4, 1951, pp. 213– 231. 13 Ladyzenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flows, 2nd ed., Gordon and Breach, New York, 1969. 14 Ladyzenskaya, O. A., Unique Solvability in the Large of Three-Dimensional Cauchy Problems for the Navier-Stokes Equations in the Presence of Axial Symmetry, in Boundary Value Problems of Mathematical Physics and Related Aspects of Function Theory, II, Steklov Inst. Seminars in Mathematics, Leningrad, Vol. 7, translated by Consultants Bureau, New York, 1970. 15 Leray, J., Sur le mouvement d'un liquide visquex emplissant l'espace, Acta Math. 63, 1934, pp. 193– 248. 16 Lin, C. S., Interpolation inequalities with weighted norms, in preparation. 17 Lions, J.-L., Quelques Methodes de Résolution des Problèmes aux Limites non Linéaires, Dunod-Gauthier-Villars, Paris, 1969. 18 Lions, J.-L., Sur la regularité et l'unicité des solutions turbulentes des équations de Navier-Stokes, Rend. Sem. Mat. Padova 30, 1960, pp. 16– 23. 19 Muckenhaupt, B., and Wheeden, R., Weighted norm inequalities for singular and fractional integrals, Trans. Amer. Math. Soc. 161, 1971, pp. 249– 258. 20 Morrey, C. B., Partial regularity results for nonlinear elliptic systems, J. Math. Mech. 17, 1968, pp. 649– 670. 21 Nirenberg, L., On elliptic partial differential equations, Ann. di Pisa 13, 1959, pp. 116– 162. 22 Ohyama, T., Interior regularity of weak solutions of the time dependent Navier-Stokes equation, Proc. Japan Acad. 36, 1960, pp. 273– 277. 23 Rivière, N. M., Singular integrals and multiplier operators, Arkiv för Mathematik 9, 1971, pp. 243– 278. 24 Scheffer, V., Turbulence and Hausdorff dimension, in Turbulence and the Navier-Stokes Equations, Lecture Notes in Math., No. 565, Springer-Verlag, 1976, pp. 94– 112. 25 Scheffer, V., Partial regularity of solutions to the Navier-Stokes equations, Pacific J. Math. 66, 1976, pp. 535– 552. 26 Scheffer, V., Hausdorff measure and the Navier-Stokes equations, Comm. Math. Phys. 55, 1977, pp. 97– 112. 27 Scheffer, V., The Navier-Stokes equations in space dimension four, Comm. Math. Phys. 61, 1978, pp. 41– 68. 28 Scheffer, V., The Navier-Stokes equations on a bounded domain, Comm. Math. Phys. 73, 1980, pp. 1– 42. 29 Serrin, J., The initial value problem for the Navier-Stokes equations, in Nonlinear Problems, R. F. Langer, Ed., Univ. of Wisconsin Press, 1963, pp. 69– 98. 30 Serrin, J., On the interior regularity of weak solutions of the Navier-Stokes equations, Arch Ration. Mech. Anal. 9, 1962, pp. 187– 195. 31 Solonnikov, V. A., Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, Trudy Mat. Inst. Steklov, Vol. 70, 1964, in Amer. Math. Soc. Translations, Series 2, Vol. 75, pp. 1– 117. 32 Solonnikov, V. A., A priori estimates for second-order parabolic equations, Trudy Mat. Inst. Steklov, Vol. 70, 1964, in Amer. Math. Soc. Trans., Series 2, 65, 1967, pp. 51– 137. 33 Stein, E., Singular Integrals and the Differentiability Properties of Functions, Princeton University Press, 1970. 34 Stein, E., Note on singular integrals, Proc. Amer. Math. Soc. 8, 1957, pp. 250– 254. 35 Témam, R., Navier-Stokes Equations. Theory and Numerical Analysis, North-Holland, Amsterdam and New York, 1977. Citing Literature Volume35, Issue6November 1982Pages 771-831 ReferencesRelatedInformation" @default.
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