Non Uniqueness of Power-Law Flows
Keyword(s):
AbstractWe apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension $$d\ge 3$$ d ≥ 3 . For the power index q below the compactness threshold, i.e. $$q \in (1, \frac{2d}{d+2})$$ q ∈ ( 1 , 2 d d + 2 ) , we show ill-posedness of Leray–Hopf solutions. For a wider class of indices $$q \in (1, \frac{3d+2}{d+2})$$ q ∈ ( 1 , 3 d + 2 d + 2 ) we show ill-posedness of distributional (non-Leray–Hopf) solutions, extending the seminal paper of Buckmaster & Vicol [10]. In this wider class we also construct non-unique solutions for every datum in $$L^2$$ L 2 .
2008 ◽
Vol 205
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pp. 187-196
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2006 ◽
Vol 316
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pp. 178-188
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2001 ◽
Vol 198
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pp. 175-196
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2010 ◽
Vol 59
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pp. 1766-1772
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2012 ◽
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pp. 285-296
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2009 ◽
Vol 58
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pp. 700-710
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2015 ◽
Vol 27
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pp. 111-130
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2003 ◽
Vol 168
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pp. 299-328
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