ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35, 76 Nagasawa, Takeyuki, Tôhoku University, Japan A new energy inequality and partial regularity for weak solutions of Navier-Stokes equations We construct weak solutions of Leray-Hopf type of 3-dimensional evolution Navier-Stokes equations by time-discretization method. Our solution satisfies an energy inequality with an extra term, which the usual energy ineuality does not have. The boundedness of the extra term gives a partial regularity reasult of weak solutions. References: [1] T. Nagasawa, Navier-Stokes flow on Riemannian manifolds, Nonlinear Anal. 30 (1997), 825–832. [2] T. Nagasawa, Construction of weak solutions of the Navier-Stokes equations on Riemannian manifold by minimizing variational functionals, to appear in Adv. Math. Sci. Appl. 9