Blow-up Solutions of the Constantin-Lax-Majda Equation with a Generalized Viscosity Term
Vol. 10 (2003), No. 1, Page 187--207.
Sakajo, Takashi
Blow-up Solutions of the Constantin-Lax-Majda Equation with a Generalized Viscosity Term
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Abstract:
A generalized one-dimensional model for the three-dimensional vorticity equation of incompressible and viscous fluid is considered. Its viscosity term is given by an arbitrary order of derivative of the vorticity. A formal solution of the equation is given explicitly by using the spectral method. We investigate convergence of the solution and show that the solution blows up in finite time for sufficiently small viscosity coefficient regardless of the order of derivative of the viscosity term.
Mathematics Subject Classification (1991): Primary 35B05; Secondary 35Q35, 76M22
Mathematical Reviews Number: MR1963803
Received: 2002-01-11
