%0 Journal Article
%T On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations
%A Dongho Chae
%J Mathematics
%D 2007
%I arXiv
%X We study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity are considered in various sense. We extend much further, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities obtained in \cite{cha1,cha2}. Some implications the notions for the 3D Navier-Stokes equations are also deduced. Generalization of the self-similar transforms is also considered, and by appropriate choice of the transform we obtain new \textit{a priori} estimates for the 3D Euler and the Navier-Stokes equations.
%U http://arxiv.org/abs/0711.1113v3