Attractors for the Navier-Stokes-Cahn-Hilliard system

Andrea Giorgini; Roger Temam

doi:10.3934/dcdss.2022118

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2022, Volume 15, Issue 8: 2249-2274. Doi: 10.3934/dcdss.2022118

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Attractors for the Navier-Stokes-Cahn-Hilliard system

Andrea Giorgini^1, , and
Roger Temam^2,

1.
Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom
2.
Institute for Scientific Computing and Applied Mathematics, Indiana University, Bloomington, IN 47405, USA

^* Corresponding author: Andrea Giorgini
^* Corresponding author: Andrea Giorgini

Dedicated to Professor Maurizio Grasselli on the occasion of his 60th birthday with friendship and best wishes

Received: January 31, 2022

Published: August 2022

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Abstract

We investigate the longtime behavior of the solutions to the Navier-Stokes-Cahn-Hilliard system (also known as Model H) with singular (e.g. Flory-Huggins) potential and non-constant viscosity. We prove that the initial and boundary value problem generates a strongly continuous semigroup on a suitable phase-space. Next, we establish the existence of the global attractor and of exponential attractors, and their regularity properties.

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Mathematics Subject Classification: 35B40, 35Q35, 35K61, 37L30, 76T06.

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