The Cauchy problem for a spin-liquid model in three space dimensions

Abstract

In this paper, we study the Cauchy problem for magnetic fluid of spin-liquid type with Mermin-Ho relation in the three-dimensional space and prove global existence and uniqueness of solutions. The proof is based on the equivalence relation between smooth solutions of the spin-liquid model and the systems of Schrödinger equations with Abelian gauge field. The Sobolev spaces with fractional derivatives are also used in our estimates.

Keywords:

• Spin-liquid model

AMS Subject Classification:

• 35Q55

Disclosure statement

No potential conflict of interest was reported by the author.