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

Abstract

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 di¤usion term on heat equations is the p-Laplacian with p b 3. This work provides a first insight towards the full case p b 2.