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References (14)
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Jinghui Zhu (2000)
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Xinfu Chen, H. Okamoto (2000)
Global existence of solutions to the Proudman-Johnson equation, 76
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On the Camassa–Holm and Hunter–Saxton equations -
Xinfu Chen, H. Okamoto (2003)
A Blow-up Problem Related to the Euler Equations of Incompressible Inviscid Fluid MotionJournal of Mathematical Sciences-the University of Tokyo, 10
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H. Okamoto, Jinghui Zhu (2000)
SOME SIMILARITY SOLUTIONS OF THE NAVIER-STOKES EQUATIONS AND RELATED TOPICSTaiwanese Journal of Mathematics, 4
- Publisher
- Springer Journals
- Copyright
- Copyright © 2007 by Birkhaueser
- Subject
- Physics; Fluid- and Aerodynamics; Mathematical Methods in Physics; Classical and Continuum Physics
- ISSN
- 1422-6928
- eISSN
- 1422-6952
- DOI
- 10.1007/s00021-007-0247-9
- Publisher site
- See Article on Publisher Site
Abstract
The generalized Proudman–Johnson equation, which was derived from the Navier–Stokes equations by Jinghui Zhu and the author, are considered in the case where the viscosity is neglected and the periodic boundary condition is imposed. The equation possesses two nonlinear terms: the convection and stretching terms. We prove that the solution exists globally in time if the stretching term is weak in the sense to be specified below. We also discuss on blow-up solutions when the stretching term is strong.
Journal
Journal of Mathematical Fluid Mechanics – Springer Journals
Published: Jun 23, 2007