Global smooth solution to the n-dimensional liquid crystal equations with fractional dissipation

Abstract

In this article, we focus on the global regularity of n-dimensional liquid crystal equations with fractional dissipation terms (−Δ)αu{\left(-\Delta )}^{\alpha }u and (−Δ)βd{\left(-\Delta )}^{\beta }d. We show that the equations have a unique global smooth solution if α≥12+n4\alpha \ge \frac{1}{2}+\frac{n}{4} and β≥12+n4\beta \ge \frac{1}{2}+\frac{n}{4}.

Keywords

• liquid crystal equations
• fractional dissipation
• global regularity
• 35q35
• 35b65
• 76a15