@article{RM_2007_62_3_a8,
author = {G. A. Seregin},
title = {Local regularity for suitable weak solutions of the {Navier{\textendash}Stokes} equations},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {595--614},
year = {2007},
volume = {62},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2007_62_3_a8/}
}
G. A. Seregin. Local regularity for suitable weak solutions of the Navier–Stokes equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 62 (2007) no. 3, pp. 595-614. http://geodesic.mathdoc.fr/item/RM_2007_62_3_a8/
[1] O. A. Ladyzhenskaya, G. A. Seregin, “On partial regularity of suitable weak solutions to the three-dimensional Navier–Stokes equations”, J. Math. Fluid Mech., 1:4 (1999), 356–387 | DOI | MR | Zbl
[2] L. Caffarelli, R.-V. Kohn, L. Nirenberg, “Partial regularity of suitable weak solutions of the Navier–Stokes equations”, Commun. Pure Appl. Math., 35:6 (1982), 771–831 | DOI | MR | Zbl
[3] J. Leray, “Sur le mouvement d'un liquide visqueux emplissant l'espace”, Acta Math., 63:1 (1934), 193–248 | DOI | MR | Zbl
[4] G. A. Seregin, “Local regularity theory of Navier–Stokes equations”, Handbook of mathematical fluid dynamics, vol. 4, eds. S. J. Friedlander, D. Serre, North-Holland, Amsterdam, 2007, 159–200 | MR
[5] F.-H. Lin, “A new proof of the Caffarelly–Kohn–Nirenberg theorem”, Commun. Pure Appl. Math., 51:3 (1998), 241–257 | 3.0.CO;2-A class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl
[6] J. Serrin, “On the interior regularity of weak solutions of the Navier–Stokes equations”, Arch. Ration. Mech. Anal., 9:1 (1962), 187–195 | DOI | MR | Zbl
[7] M. Struwe, “On partial regularity results for the Navier–Stokes equations”, Commun. Pure Appl. Math., 41:4 (1988), 437–458 | DOI | MR | Zbl
[8] G. Seregin, V. Šverák, “The Navier–Stokes equations and backward uniqueness”, Nonlinear problems in mathematical physics, II, In honor of Professor O. A. Ladyzhenskaya, Int. Math. Ser. (N. Y.), 2, Kluwer, New York, 2002, 359–370 | MR | Zbl
[9] L. Iskauriaza, G. A. Seregin, V. Shverak, “$L_{3,\infty}$-resheniya uravnenii Nave–Stoksa i obratnaya edinstvennost”, UMN, 58:2(350) (2003), 3–44 | MR | Zbl
[10] G. A. Seregin, “On smoothness of $L_{3,\infty}$-solutions to the Navier–Stokes equations up to boundary”, Math. Ann., 332:1 (2005), 219–238 | DOI | MR | Zbl
[11] G. A. Seregin, “Otsenki podkhodyaschikh slabykh reshenii v prostranstvakh Morri s kriticheskim pokazatelem”, Zapiski nauch. sem. POMI, 336 (2006), 199–210 ; G. A. Seregin, “Estimates of suitable weak solutions to the Navier–Stokes equations in critical Morrey spaces”, J. Math. Sci., 143:2 (2007), 2961–2968 | MR | Zbl | DOI
[12] H. L. Choe, J. L. Lewis, “On the singular set in the Navier–Stokes equations”, J. Funct. Anal., 175:2 (2000), 348–369 | DOI | MR | Zbl
[13] O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Uraltseva, Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Fizmatlit, M., 1967 ; O. A. Ladyzhenskaya, V. A. Solonnikov, N. N. Ural'tceva, Linear and quasi-linear equations of parabolic type, Transl. Math. Monogr., 23, Amer. Math. Soc., Providence, 1968 | MR | MR | Zbl
[14] A. A. Kiselev, O. A. Ladyzhenskaya, “O suschestvovanii i edinstvennosti nestatsionarnoi zadachi dlya vyazkoi neszhimaemoi zhidkosti”, Izv. AN SSSR. Ser. matem., 21 (1957), 655–680 ; A. A. Kiselev, O. A. Ladyzhenskaya, “On the existence and uniqueness of solutions of the non-stationary problems for flows of non-compressible fluids”, Amer. Math. Soc. Transl. Ser. 2, 24 (1963), 79–106 | MR | Zbl | Zbl