On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five
| Autor: | Xiao Li Guo, Yue Yang Men |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Mathematical analysis Zero (complex analysis) Non-dimensionalization and scaling of the Navier–Stokes equations 01 natural sciences Fractional power Dimension (vector space) 0103 physical sciences Hausdorff measure 010307 mathematical physics 0101 mathematics Navier–Stokes equations Laplace operator Mathematics |
| Zdroj: | Acta Mathematica Sinica, English Series. 33:1632-1646 |
| ISSN: | 1439-7617 1439-8516 |
| DOI: | 10.1007/s10114-017-7125-z |
| Popis: | In this paper, we investigate the partial regularity of suitable weak solutions to the multi-dimensional stationary Navier–Stokes equations with fractional power of the Laplacian (−Δ) α (n/6 ≤ α < 1 and α ≠ 1/2). It is shown that the n + 2 − 6α (3 ≤ n ≤ 5) dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in e-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20]. |
| Databáze: | OpenAIRE |
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