کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4610639 | 1338576 | 2014 | 26 صفحه PDF | دانلود رایگان |
The partial regularity of the suitable weak solutions to the Navier–Stokes equations in RnRn with n=2,3,4n=2,3,4 and the stationary Navier–Stokes equations in RnRn for n=2,3,4,5,6n=2,3,4,5,6 are investigated in this paper. Using some elementary observation of these equations together with De Giorgi iteration method, we present a unified proof on the results of Caffarelli, Kohn and Nirenberg [1], Struwe [17], Dong and Du [5], and Dong and Strain [7]. Particularly, we obtain the partial regularity of the suitable weak solutions to the 4d non-stationary Navier–Stokes equations, which improves the previous result of [5], where Dong and Du studied the partial regularity of smooth solutions of the 4d Navier–Stokes equations at the first blow-up time.
Journal: Journal of Differential Equations - Volume 256, Issue 3, 1 February 2014, Pages 1224–1249