A Study On The Two Component Periodic Shallow Water Systems

Author

Caixia Chen

Graduation Semester and Year

2012

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Yue Liu

Abstract

In this dissertation we study the generalized periodic two-component Camassa-Holm system and the generalized periodic two-component Dullin-Gottwald-Holm system, which can be derived from the Euler equation with nonzero constant vorticity in shallow water waves moving over a linear shear flow. The precise blow-up scenarios of strong solutions and several results of blow-up solutions with certain initial profiles are described in detail. The exact blow-up rates are also determined. Finally, the sufficient conditions for global solutions are established.

Disciplines

Mathematics | Physical Sciences and Mathematics

License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

Comments

Degree granted by The University of Texas at Arlington

Recommended Citation

Chen, Caixia, "A Study On The Two Component Periodic Shallow Water Systems" (2012). Mathematics Dissertations. 159.
https://mavmatrix.uta.edu/math_dissertations/159