A Blow-up Problem Related to the Euler Equations of Incompressible Inviscid Fluid Motion
Vol. 10 (2003), No. 2, Page 373--389.
Chen, Xinfu ; Okamoto, Hisashi
A Blow-up Problem Related to the Euler Equations of Incompressible Inviscid Fluid Motion
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Abstract:
We study the blow-up of a certain system of ODEs which are coupled in such a way that the "total mass" is preserved. The system of ODEs is a model proposed by the second author and J. Zhu in order to demonstrate the importance of the convection term in the Proudman-Johnson equation, which describes the motion of incompressible fluid. In the present paper, we derive a necessary and sufficient condition for blow-up of solutions, and we provide long time or near blow-up time asymptotic behavior.
Mathematics Subject Classification (1991): 35Q35, 76B03
Mathematical Reviews Number: MR1987137
Received: 2002-06-17
