On the Lagrangian dynamics of the axisymmetric 3D Euler equations |
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Authors: | Dongho Chae |
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Institution: | Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea |
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Abstract: | We study the dynamics along the particle trajectories for the 3D axisymmetric Euler equations. In particular, by rewriting the system of equations we find that there exists a complex Riccati type of structure in the system on the whole of R3, which generalizes substantially the previous results in 5] (D. Chae, On the blow-up problem for the axisymmetric 3D Euler equations, Nonlinearity 21 (2008) 2053-2060). Using this structure of equations, we deduce the new blow-up criterion that the radial increment of pressure is not consistent with the global regularity of classical solution. We also derive a much more refined version of the Lagrangian dynamics than that of 6] (D. Chae, On the Lagrangian dynamics for the 3D incompressible Euler equations, Comm. Math. Phys. 269 (2) (2007) 557-569) in the case of axisymmetry. |
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Keywords: | 35Q35 76B03 |
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