2017/12/28 by Ning Jiang, Jiang, Ning, Yi-Long Luo +3 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.1712.09799
openalex publication_date 2017/12/28 · openalex created_date 2018/01/05 · openalex updated_date 2026/07/28
We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case \citeJiang-Luo-arXiv-2017 and some techniques from compressible Navier-Stokes equations, we prove the local-in-time existence of the classical solution to the system with finite initial energy, under some constraints on the Leslie coefficients which ensure the basic energy law is dissipative. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the global classical solution can be established.