Xingyou Zhang

Citation

Thesis Title
Dynamics and Numerics of Generalized Euler Equations

Read article at Massey Research Online:

Mr Zhang investigated the mathematical and dynamic properties of some motion equations of mathematical physics known as generalised Euler equations. Members of this family include equations used in hydrodynamics, oceanography, micro-magnetism and medical imaging. Generalised Euler equations describe straight line motion on various curved spaces. Mr Zhang proved several theorems on the existence, uniqueness and other properties of solutions to a family of equations known as modified Camassa-Holm equations. He also discovered a novel phenomenon in which isolated waves called solitons emerge by a previously unknown mechanism. The formation of solitons was studied analytically, numerically, and by using the technique of matched asymptotic expansion, leading to the identification of several unusual features. These features are likely to be relevant to the behaviour of many other Euler equations.

Supervisors
Distinguished Professor Robert McLachlan
Dr Matthew Perlmutter