ABSTRACT
We shall investigate the existence, uniqueness and regularity of global solutions to a Cauchy problem for a square phase crystal field model with applications to crystal dynamics. To prove the existence of weak solutions we employ the energy method, and to investigate the regularity of solutions we make use of various techniques to derive delicate a priori estimates.
Acknowledgments
I would like to sincerely appreciate Professor P. Zhu for his careful instruction and discussions.
Disclosure statement
No potential conflict of interest was reported by the author(s).