Graduation Semester and Year
2018
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Yue Liu
Abstract
In this thesis, we study a mathematical model of long-crested water waves propagating in one direction with the effect of Earth's rotation near the equator by following the formal asymptotic procedures. Firstly, we derive a new model equation called the rotational b-family of equations by using the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations. Secondly,we establish that the local well-posedness of the Cauchy problem for the rotational b-family of equations on the Sobolev space H⁸, for s > 3=2. In addition, we study the effects of the Coriolis force and nonlocal higher nonlinearities on blow-up criteria and wave-breaking phenomena.
Keywords
Coriolis effect, B-family of equations
Disciplines
Mathematics | Physical Sciences and Mathematics
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Bolat, Emel, "A study on the rotational b-family of equations" (2018). Mathematics Dissertations. 235.
https://mavmatrix.uta.edu/math_dissertations/235
Comments
Degree granted by The University of Texas at Arlington