Abstract
In this chapter we investigate the properties of solutions to a system of partial differential equations motivated by the Navier-Stokes equations and ramifications of these which arise in various thermal convection contexts. In addition to studying blow-up (or non-existence) we also examine when the solution will remain bounded for all time, or even decay. The study of the system is of interest in its own right, and we have not seen this particular investigation elsewhere. The results reported here are an extension of sections 2.3-2.6 of Straughan (1992), and in places are an extension of Ames & Straughan (1995) and Levine et al. (1989).
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© 1998 Springer-Verlag Berlin Heidelberg
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Straughan, B. (1998). Analysis of a First-Order System. In: Explosive Instabilities in Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58807-5_2
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DOI: https://doi.org/10.1007/978-3-642-58807-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63740-7
Online ISBN: 978-3-642-58807-5
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