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 .