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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 5
44
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Original Articles

On the shallow water equations with periodicity in one direction

Pages 537-553 | Received 10 Nov 2006, Accepted 15 Nov 2006, Published online: 30 May 2007
 

Abstract

The linearized 2D shallow water equations, supplemented with suitable boundary conditions in one direction and periodicity in the other direction are considered. The well-posedness of this mixed boundary value problem is proven, using the linear semi-group theory. The well-posedness of the totally periodic problem is also proven.

Acknowledgements

This work was partially supported by the NSF grant DMS-0305110, and by the Research Fund of Indiana University. The author is very thankful to Professor Roger Temam for suggesting this problem and for his helpful advice in its resolution.

Notes

1 Here denotes the Schwartz space of C functions with compact support in .

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