Description
The dissipative shallow-water equations (SWE) possess both real-world application and extensive analysis in theoretical partial differential equations. This analysis is dominated by modeling the dissipation as diffusion, with its mathematical representation being the Laplacian. However, the usage of the biharmonic as a dissipative operator by oceanographers and atmospheric scientists and its underwhelming amount of analysis indicates a gap in SWE theory. In order to provide rigorous mathematical justification for the utilization of these equations in simulations with real-world implications, we extend an energy method utilized by Matsumura and Nishida for initial value problems relating to the equations of motion for compressible, vsicous, heat-conductive fluids ([6], [7]) and applied by Kloeden to the diffusive SWE ([4]) to prove global time existence of classical solutions to the biharmonic SWE. In particular, we develop appropriate a priori growth estimates that allow one to extend the solution's temporal existence infinitely under sufficient constraints on initial data and external forcing, resulting in convergence to steady-state.
Download count: 1
Details
Title
- Asymptotic Stability of Biharmonic Shallow Water Equations
Contributors
- Kofroth, Collin Michael (Author)
- Jones, Don (Thesis director)
- Smith, Hal (Committee member)
- School of Mathematical and Statistical Sciences (Contributor)
- Barrett, The Honors College (Contributor)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2017-05
Resource Type
Collections this item is in