On Formation of a Locally Self-Similar Collapse in the Incompressible Euler Equations

초록

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 and , then the blow-up does not occur, provided or . This includes the L (3) case natural for the Navier-Stokes equations. For we exclude profiles with asymptotic power bounds of the form . Solutions homogeneous near infinity are eliminated, as well, except when homogeneity is scaling invariant.

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