2017 年 60 巻 1 号 p. 1-20
This paper is concerned with a system of p-Laplace heat equations with constraints and Navier-Stokes equations. The existence and uniqueness of solutions have been already proved for several types of the system in 2-dimensional domains. This paper gives the existence result in 3-dimensional domains, where the diffusion term on heat equations is the p-Laplacian with p ≥ 3. This work provides a first insight towards the full case p ≥ 2.