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On the Viscous Cahn-Hilliard-Oono System with Chemotaxis and Singular Potential
  • Jingning He
Jingning He
Fudan University - Handan Campus

Corresponding Author:[email protected]

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We analyze a diffuse interface model that couples a viscous Cahn-Hilliard equation for the phase variable with a diffusion-reaction equation for the nutrient concentration. The system under consideration also takes into account some important mechanisms like chemotaxis, active transport as well as nonlocal interaction of Oono’s type. When the spatial dimension is three, we prove the existence and uniqueness of global weak solutions to the model with singular potentials including the physically relevant logarithmic potential. Then we obtain some regularity properties of the weak solutions when t>0. In particular, with the aid of the viscous term, we prove the so-called instantaneous separation property of the phase variable such that it stays away from the pure states ±1 as long as t>0. Furthermore, we study long-time behavior of the system, by proving the existence of a global attractor and characterizing its ω-limit set.
26 May 2021Submitted to Mathematical Methods in the Applied Sciences
27 May 2021Submission Checks Completed
27 May 2021Assigned to Editor
29 May 2021Reviewer(s) Assigned
26 Jul 2021Review(s) Completed, Editorial Evaluation Pending
27 Jul 2021Editorial Decision: Revise Major
08 Sep 20211st Revision Received
08 Sep 2021Assigned to Editor
08 Sep 2021Submission Checks Completed
10 Sep 2021Reviewer(s) Assigned
12 Sep 2021Review(s) Completed, Editorial Evaluation Pending
22 Sep 2021Editorial Decision: Revise Minor
30 Oct 20212nd Revision Received
30 Oct 2021Submission Checks Completed
30 Oct 2021Assigned to Editor
01 Nov 2021Reviewer(s) Assigned
01 Nov 2021Review(s) Completed, Editorial Evaluation Pending
03 Nov 2021Editorial Decision: Accept
15 May 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 7 on pages 3732-3763. 10.1002/mma.8014