Solvability of       $p$-Laplacian parabolic logistic equations       with constraints coupled with       Navier-Stokes       equations in 2D domains

Yutaka Tsuzuki

doi:10.3934/eect.2014.3.191

Article Contents

2014, Volume 3, Issue 1: 191-206. Doi: 10.3934/eect.2014.3.191

This issue Previous Article Boundary approximate controllability of some linear parabolic systems Next Article

Solvability of $p$-Laplacian parabolic logistic equations with constraints coupled with Navier-Stokes equations in 2D domains

Yutaka Tsuzuki^1,

1.
Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601

Received: March 31, 2013

Revised: July 31, 2013

Published: February 2014

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Abstract

This paper is concerned with the system of nonlinear heat equations with constraints coupled with Navier-Stokes equations in two-dimensional domains. In 2012, Sobajima, Tsuzuki and Yokota proved the existence and uniqueness of solutions to the system with heat equations including the diffusion term $\Delta\theta$, where $\theta$ represents the temperature. This paper gives the existence result in which the Laplace operator $\Delta$ is replaced with the $p$-Laplace operator $\Delta\rho$, where $p>2$.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 47H05.

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