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Some remarks on a Neumann boundary value problem arising in fluid dynamics
Published online by Cambridge University Press: 17 February 2009
Abstract
It is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.
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- Copyright © Australian Mathematical Society 2004
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