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- W3104853313 abstract "In this note, we show that Luo-Hou’s ansatz for the self-similar solution to the axisymmetric solution to the 3D Euler equations leads to triviality of the solution under suitable decay condition of the blow-up profile. The equations for the blow-up profile reduces to an over-determined system of partial differential equations, whose only solution with decay is the trivial solution. We also propose a generalization of Luo-Hou’s ansatz. Using the vanishing of the normal velocity at the boundary, we show that this generalized self-similar ansatz also leads to a trivial solution. These results show that the self-similar ansatz may be valid either only in a time-dependent region which shrinks to the boundary circle at the self-similar rate, or under different boundary conditions at spatial infinity of the self-similar profile." @default.
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- W3104853313 date "2014-10-21" @default.
- W3104853313 modified "2023-09-23" @default.
- W3104853313 title "Remark on Luo-Hou’s Ansatz for a Self-similar Solution to the 3D Euler Equations" @default.
- W3104853313 cites W2038604285 @default.
- W3104853313 doi "https://doi.org/10.1007/s00332-014-9225-6" @default.
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