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Research Article | Open Access

Attractors for a Navier–Stokes–Allen–Cahn system with unmatched densities

Chunyou Sun1,2, Junyan Tan1( )
School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R. China
School of Mathematics and Statistics, Donghua University, Shanghai, 201620, P.R. China
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Abstract

This paper investigates the long-time behavior for a Navier–Stokes–Allen–Cahn system, a diffuse interface model for two-phase incompressible flows with unmatched densities, non-constant viscosities, and a singular Flory–Huggins potential. First, we establish the dissipativity of strong solutions via some a priori estimates. Then, we demonstrate the regular-continuity of the semigroup, which allows us to prove the existence of the global attractor in the strong solutions space.

Keywords

two phase flowglobal attractorNavier–Stokes–Allen–Cahn systemdissipativitysingular Flory–Huggins potential
CLC number: 35B40, 35Q35, 35K61, 76T06

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Communications in Analysis and Mechanics
Volume 17 Issue 1,
March 2025
Pages 237-262
DOI: 10.3934/cam.2025010

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Cite this article:
Sun C, Tan J. Attractors for a Navier–Stokes–Allen–Cahn system with unmatched densities. Communications in Analysis and Mechanics, 2025, 17(1): 237-262. https://doi.org/10.3934/cam.2025010

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Received: 26 January 2025
Revised: 04 March 2025
Accepted: 07 March 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)