Takashi Sakajo 2003 Nonlinearity 16 1319 doi:10.1088/0951-7715/16/4/307
Takashi Sakajo
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We consider a one-dimensional model for the three-dimensional vorticity equation of incompressible and viscous fluids. This model is obtained by adding a generalized viscous diffusion term to the Constantin–Lax–Majda equation, which was introduced as a model for the three-dimensional Euler equation (Constantin P, Lax P D and Majda A 1985 A simple one-dimensional model for the three-dimensional vorticity equation Commun. Pure. Appl. Math. 38 715–24). It is shown in Sakajo T (2003 Blow-up solutions of the Constantin–Lax–Majda equation with a generalized viscosity term J. Math. Sci. Univ. Tokyo 10 187–207) that the solution of the model equation blows up in finite time for sufficiently small viscosity, however large a diffusion term it may have. In this paper, we discuss the existence of a unique global solution for large viscosity.
47.57.eb Diffusion and aggregation
47.32.-y Vortex dynamics; rotating fluids
47.10.ad Navier-Stokes equations
02.60.Lj Ordinary and partial differential equations; boundary value problems
76R50 Diffusion (See also 60J60)
35Q35 Other equations arising in fluid mechanics
Issue 4 (July 2003)
Received 28 January 2003, in final form 28 March 2003
Published 6 May 2003
Takashi Sakajo 2003 Nonlinearity 16 1319
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