Time-periodic solution to a three-phase model of viscoelastic fluid flow
Chengxin Du, Changchun Liu, Ming Mei · Discrete and Continuous Dynamical Systems · 2022
This paper is concerned with a three-phase model of viscoelastic fluid flow in $ \mathbb{R}^N $ for $ N\geq 5 $. We first prove the existence of the time-periodic solution to the integral system in the space of $ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $. Then we further show the existence, uniqueness and regularity of the mild solution of the problem. Finally we confirm that such a mild solution is a strong solution in the space of $ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $. The proof is based on the compactness analysis with some new development, where a new estimate scheme is artfully constructed.