Lin, Fanghua A new proof of the Caffarelli-Kohn-Nirenberg theorem. (English) Zbl 0958.35102 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) Cited in 1 ReviewCited in 265 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI