A study on the rotational b-family of equations

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.