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- W2072138519 abstract "The paper addresses the question of the existence of a locally self-similar blow-up for the incompressible Euler equations. Several exclusion results are proved based on the L p -condition for velocity or vorticity and for a range of scaling exponents. In particular, in N dimensions if in self-similar variables $${u in L^p}$$ and $${u sim frac{1}{t^{alpha/(1+alpha)}}}$$ , then the blow-up does not occur, provided $${alpha > N/2}$$ or $${-1 < alpha leq N,/p}$$ . This includes the L 3 case natural for the Navier–Stokes equations. For $${alpha = N,/2}$$ we exclude profiles with asymptotic power bounds of the form $${ |y|^{-N-1+delta} lesssim |u(y)| lesssim |y|^{1-delta}}$$ . Solutions homogeneous near infinity are eliminated, as well, except when homogeneity is scaling invariant." @default.
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- W2072138519 date "2013-05-15" @default.
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- W2072138519 title "On Formation of a Locally Self-Similar Collapse in the Incompressible Euler Equations" @default.
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- W2072138519 doi "https://doi.org/10.1007/s00205-013-0630-z" @default.
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