Author

Emel Bolat

ORCID Identifier(s)

0000-0002-9705-9556

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

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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