A new regularity criterion for weak solutions to the Navier–Stokes equations
Tóm tắt
Từ khóa
Tài liệu tham khảo
Beirão da Veiga, 1995, A new regularity class for the Navier–Stokes equations in Rn, Chinese Ann. Math., 16, 407
Beirão da Veiga, 2000, A sufficient condition on the pressure for the regularity of weak solutions to the Navier–Stokes equations, J. Math. Fluid Mech., 2, 99, 10.1007/PL00000949
Beirao da Veiga, 2000, On the smoothness of a class of weak solutions to the Navier–Stokes equations, J. Math. Fluid Mech., 2, 315, 10.1007/PL00000955
Berselli, 2002, Regularity criteria involving the pressure for the weak solutions to the Navier–Stokes equations, Proc. Amer. Math. Soc., 130, 3585, 10.1090/S0002-9939-02-06697-2
Caffarelli, 1982, Partial regularity of suitable weak solutions of the Navier–Stokes equations, Comm. Pure Appl. Math., 35, 771, 10.1002/cpa.3160350604
Chae, 1999, On the regularity criterion for the solutions of the Navier–Stokes equations, Electron. J. Differential Equations, 1999, 1, 10.1006/jdeq.1998.3607
Chae, 2001, Regularity criterion in terms of pressure for the Navier–Stokes equations, Nonlinear Anal. Ser. A: Theory Methods, 46, 727, 10.1016/S0362-546X(00)00163-2
Giga, 1986, Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier–Stokes system, J. Differential Equations, 62, 186, 10.1016/0022-0396(86)90096-3
He, 2002, Regularity for solutions to the Navier–Stokes equations with one velocity component regular, Electron. J. Differential Equations, 29, 1
Hopf, 1951, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4, 213, 10.1002/mana.3210040121
Kozono, 1997, Regularity criterion on weak solutions to the Navier–Stokes equations, Adv. Differential Equations, 2, 535, 10.57262/ade/1366741147
Kozono, 2000, Bilinear estimates in BMO and the Navier–Stokes equations, Math. Z., 235, 173, 10.1007/s002090000130
Leray, 1934, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math., 63, 193, 10.1007/BF02547354
J. Neustupa, A. Novotný, P. Penel, An interior regularity of a weak solution to the Navier–Stokes equations in dependence on one component of velocity, Preprint, 2001
Scheffer, 1976, Partial regularity of solutions to the Navier–Stokes equations, Pacific J. Math., 66, 535, 10.2140/pjm.1976.66.535
Serrin, 1962, On the interior regularity of weak solutions of the Navier–Stokes equations, Arch. Rational Mech. Anal., 9, 187, 10.1007/BF00253344
Sohr, 2001, A regularity class for the Navier–Stokes equations in Lorentz spaces, J. Evolution Equations, 1, 441, 10.1007/PL00001382
H. Sohr, A generalization of Serrin's regularity criterion for the Navier–Stokes equations, Quaderni Di Math. (2002), in press
Struwe, 1988, On partial regularity results for the Navier–Stokes equations, Comm. Pure Appl. Math., 41, 437, 10.1002/cpa.3160410404
Temam, 2001
Tian, 1999, Gradient estimation on Navier–Stokes equations, Comm. Anal. Geo., 7, 221, 10.4310/CAG.1999.v7.n2.a1
von Wahl, 1986, Regularity of weak solutions of the Navier–Stokes equations, vol. 45, 497
von Wahl, 1985, The Equations of Navier–Stokes and Abstract Parabolic Equations, vol. E8
Zhou, 2002, A new regularity criterion for the Navier–Stokes equations in terms of the gradient of one velocity component, Methods Appl. Anal., 9, 563, 10.4310/MAA.2002.v9.n4.a5
Zhou, 2004, Regularity criteria in terms of pressure for the 3-D Navier–Stokes equations in a generic domain, Math. Ann., 328, 173, 10.1007/s00208-003-0478-x
Y. Zhou, Regularity criteria for Navier–Stokes equations in term of pressure in R3, Proc. Amer. Math. Soc. (2005), in press