Regularity of Navier-Stokes flows with bounds for the pressure
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- 作者：Chuong V. Trana ; cvt1@st-andrews.ac.uk ; Xinwei Yub ; xinweiyu@math.ualberta.ca
- 关键词：Navier&ndash ; Stokes equations ; Hö ; lder continuity ; Global regularity
- 刊名：Applied Mathematics Letters
- 出版年：2017
- 出版时间：May 2017
- 年：2017
- 卷：67
- 期：Complete
- 页码：21-27
- 全文大小：787 K
- 卷排序：67
文摘
This study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t)≔{x:|u(x,t)|>c∥u∥Lr(R3)}Ω(t)≔{x:|u(x,t)|>cuLr(R3)}, for some r≥3r≥3 and constant cc independent of tt, with measure |Ω||Ω|. It is shown that if ∥p+P∥L3∕2(Ω)p+PL3∕2(Ω) becomes sufficiently small as |Ω||Ω| decreases, then ∥u∥L(r+6)∕3(R3)uL(r+6)∕3(R3) decays and regularity is secured. Here pp is the physical pressure and PP is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p+P||p+P| within ΩΩ are deduced.
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