ISSN:
1422-6952
Keywords:
Keywords. Navier—Stokes equations, regularity, projection.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract. We improve regularity criteria for weak solutions to the Navier-Stokes equations stated in references [1], [3] and [12], by using in the proof given in [3], a new idea introduced by H. O. Bae and H. J. Choe in [1]. This idea allows us, in one of the main hypothesis (see eq. (1.7)), to replace the velocity u by its projection $ \bar u $ into an arbitrary hyperplane of $ {\Bbb R}^n $ ; see Theorem A. For simplicity, we state our results for space dimension $ n \le 4 $ , since if $ n \ge 5 $ the proofs become more technical and additional hypotheses are needed. However, for the interested reader, we will present the formal calculations for arbitrary dimension n.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00000955
