On partial regularity results for the navier‐stokes equations

Looking at the regularity results of Scheffer, respectively, Caffarelli, Kohn and Nirenberg from a new point of view indicates that estimates for the pressure do not play an essential role in partial regularity results for the Navier-Stokes equations.

[1]  Yoshikazu Giga,et al.  Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system , 1986 .

[2]  Vladimir Scheffer.  Partial regularity of solutions to the Navier-Stokes equations. , 1976 .

[3]  S. Agmon,et al.  Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I , 1959 .

[4]  B. Jones,et al.  The initial value problem for the Navier-Stokes equations with data in Lp , 1972 .

[5]  Jean Leray,et al.  Sur le mouvement d'un liquide visqueux emplissant l'espace , 1934 .

[6]  J. Serrin.  On the interior regularity of weak solutions of the Navier-Stokes equations , 1962 .

[7]  Takehiko Ohyama,et al.  Interior regularity of weak solutions of the time-dependent Navier-Stokes equation , 1960 .

[8]  Mariano Giaquinta,et al.  Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 , 1984 .

[9]  Vladimir Scheffer.  A solution to the Navier-Stokes inequality with an internal singularity , 1985 .

[10]  E. Hopf,et al.  Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet , 1950 .

[11]  H. Beckert,et al.  J. L. Lions and E. Magenes, Non‐Homogeneous Boundary Value Problems and Applications, II. (Die Grundlehren d. Math. Wissenschaften, Bd. 182). XI + 242 S. Berlin/Heidelberg/New York 1972. Springer‐Verlag. Preis geb. DM 58,— , 1973 .

[12]  Wolf von Wahl,et al.  The equations of Navier-Stokes and abstract parabolic equations , 1985 .

[13]  C. B. Morrey.  Multiple Integrals in the Calculus of Variations , 1966 .

[14]  Stationary solutions to the Navier-Stokes equations in dimension four , 1979 .

[15]  Wolf von Wahl,et al.  On the regularity of the pressure of weak solutions of Navier-Stokes equations , 1986 .

[16]  R. Kohn,et al.  Partial regularity of suitable weak solutions of the navier‐stokes equations , 1982 .