A new proof of the Caffarelli-Kohn-Nirenberg theorem. (English) Zbl 0958.35102

Lin, Fanghua

Commun. Pure Appl. Math. 51, No. 3, 241-257 (1998).

The paper is concerned with the regularity of weak solutions to the nonstationary incompressible Navier-Stokes equations, in particular with the partial regularity for solutions of the Cauchy problem in three spatial dimensions. The author gives a new proof of the main results that are due to L. Caffarelli, R. Kohn, and L. Nirenberg [Commun. Pure Appl. Math. 35, 771-831 (1982; Zbl 0509.35067)]. In doing so he uses an estimate by H. Sohr and W. von Wahl [Arch. Math. 46, 428-439 (1986; Zbl 0574.35070)] on the pressure.
In this paper the author gives a clear presentation of the problem as well as of the results which are still the best that were proven.

Reviewer: J.Bemelmans (Aachen)

MSC:

35Q30	Navier-Stokes equations
35D10	Regularity of generalized solutions of PDE (MSC2000)

Keywords:

Navier-Stokes equations; partial regularity

Citations:

Zbl 0509.35067; Zbl 0574.35070