2018/01/08 by Wei Luo, Zhaoyang Yin, Luo, Wei +1
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.1801.02285
In this paper we mainly investigate the Cauchy problem of the Doi-Edwards polymer model with dimension d≥2. The model was derived in the late 1970s to describe the dynamics of polymers in melts. The system contain a Navier-Stokes equation with an additional stress tensor which depend on the deformation gradient tensor and the memory function. The deformation gradient tensor satisfies a transport equation and the memory function satisfies a degenerate parabolic equation. We first proved the local well-posedness for the Doi-Edwards polymer model in Besov spaces by using the Littlewood-Paley theory. Moreover, if the initial velocity and the initial memory is small enough, we obtain a global existence result.