Previous |  Up |  Next


Navier-Stokes equations; regularity of weak solutions; regular and singular points
In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.
[1] L.  Caffarelli, R.  Kohn and L.  Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Comm. Pure Appl. Math. 35 (1982), 771–831. DOI 10.1002/cpa.3160350604 | MR 0673830
[2] A. P.  Calderón, A.  Zygmund: On singular integrals. Amer. J.  Math. 78 (1956), 289–309. DOI 10.2307/2372517 | MR 0084633
[3] C.  Foias, R.  Temam: Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J.  Math. Pures Appl. 58 (1979), 339–368. MR 0544257
[4] G. P.  Galdi: An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I: Linearized and Steady Problems; Vol. II: Nonlinear Steady Problems. Springer-Verlag, New York-Berlin-Heidelberg, 1994. MR 1284205
[5] H.  Kozono: Removable singularities of weak solutions to the Navier-Stokes equations. Comm. Partial Differential Equations 23 (1998), 949–966. DOI 10.1080/03605309808821374 | MR 1632780 | Zbl 0910.35090
[6] 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 (1999), 356–387. DOI 10.1007/s000210050015 | MR 1738171
[7] J.  Serrin: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 9 (1962), 187–195. DOI 10.1007/BF00253344 | MR 0136885 | Zbl 0106.18302
[8] Y.  Taniuchi: On generalized energy equality of the Navier-Stokes equations. Manuscripta Math. 94 (1997), 365–384. DOI 10.1007/BF02677860 | MR 1485443 | Zbl 0896.35106
[9] R.  Temam: The Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland Publishing Company, Amsterodam-New York-Oxford, 1979. MR 0603444
Partner of
EuDML logo