An estimate on the parabolic fractal dimension of the singular set for solutions of the Navier-Stokes system

作者：Kukavica Igor^*; Pei Yuan

来源：Nonlinearity, 2012, 25(9): 2775-2783.

DOI：10.1088/0951-7715/25/9/2775

We estimate the parabolic fractal (or parabolic box-counting) dimension of the singular set for suitable weak solutions of the Navier-Stokes equations in a bounded domain D. We prove that the parabolic fractal dimension is bounded by 45/29 improving an earlier result from (Kukavica 2009 Nonlinearity 22 2889-900). Also, we introduce the new (parabolic) lambda-fractal dimension, where lambda is a parameter, which for lambda = 1 agrees with the parabolic fractal and for lambda = infinity with the parabolic Hausdorff dimension. We prove that for a certain range of lambda, the dimension of the singular set is bounded by 3/2.

• 出版日期2012-9