On the generalized self-similar singularities for the Euler and the Navier-Stokes equations |
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Authors: | Dongho Chae |
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Affiliation: | Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea |
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Abstract: | In this paper we study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the Euler and the Navier-Stokes equations, where the sense of convergence and self-similarity are considered in various generalized senses. We improve substantially, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities. Generalization of the self-similar transforms is also considered, and by appropriate choice of the parameterized transform we obtain new a priori estimates for the Euler and the Navier-Stokes equations depending on a free parameter. |
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Keywords: | Euler equations Navier-Stokes equations Generalized self-similar singularities A priori estimates |
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