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Conformal maps and reductions of the Benney equations

✍ Scribed by John Gibbons; Serguei P. Tsarev

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
78 KB
Volume
258
Category
Article
ISSN
0375-9601

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✦ Synopsis

We consider Benney's equations, and their reductions to systems with finitely many Riemann invariants. The equations w x describing these reductions were given in 5 and a construction of a class of their solutions was briefly described there. Here we discuss the properties of these equations in more detail, and investigate the relationship between these and Loewner's w x 10 theory of conformal mappings of slit domains. A dense family of explicit solutions is constructed.

πŸ“œ SIMILAR VOLUMES

Reductions of the Benney equations
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✍ H.A Biagioni; F Linares πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 281 KB

We establish global well-posedness for the initial value problem IVP associated to the so-called Benney᎐Lin equation. This model is a Korteweg᎐de Vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics. We also study the limiting behaviour of solutions to this IV