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

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.


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