Existence and regularity of global solutions to a Cauchy problem for a square phase-field crystal model

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.

KEYWORDS:

• Crystal symmetry
• phase-field crystal model
• Cauchy problem
• global weak solutions
• regularity

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35A01
• 35D30

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).

Additional information

Funding

The author is supported in part by the Science and Technology Commission of Shanghai Municipality [grant number 20JC1413600].