Solvability of p-Laplacian Parabolic Equations with Constraints Coupled with Navier-Stokes Equations in 3D Domains by Using Largeness of p

Abstract

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.