可压缩向列型液晶流体的适定性

On the well-posedness for the compressible nematic liquid crystal flow

本文研究多维(N 2)可压缩向列型液晶流体的Cauchy问题,在初始密度远离真空这个自然的条件下,借助于Littlewood-Paley理论和Schauder-Tychonoff不动点定理,在基于Lp框架下的临界Besov空间中证明大初值意义下可压缩向列型液晶模型强解的局部存在性和唯一性.

The Cauchy problem for the compressible flow of nematic liquid crystals in dimension（N 2） is considered. Employing the Littlewood-Paley theory and Schauder-Tychonoff fixed point theorem, we prove the local well-posedness of the system for large initial data in critical Besov spaces based on the Lpframework under the sole natural assumption that the initial density is bounded away from zero.