Global well-posedness of a Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential in 2D

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:297

Article

He, Jingning¹  Wu, Hao^1,2,3 

[1] Fudan Univ, Sch Math Sci, Handan Rd 220, Shanghai 200433, Peoples R China

[2] Fudan Univ, Shanghai Key Lab Contemporary Appl Math, Handan Rd 220, Shanghai 200433, Peoples R China

[3] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Handan Rd 220, Shanghai 200433, Peoples R China

关键词: Navier-Stokes-Cahn-Hilliard system;    Chemotaxis;    Active transport;    Singular potential;    Global strong solutions;    Separation property;   

DOI  :  10.1016/j.jde.2021.06.022

来源: Elsevier

【 摘 要 】

We study a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effects. This model also takes into account some significant mechanisms such as active transport and nonlocal interactions of Oono's type. The system under investigation couples the Navier-Stokes equations for the fluid velocity, a convective Cahn-Hilliard equation with physically relevant singular potential for the phase-field variable and an advection-diffusion-reaction equation for the nutrient density. For the initial boundary value problem in a smooth bounded domain Omega subset of R-2, we first prove the existence and uniqueness of global strong solutions that are strictly separated from the pure states +/- 1 over time. Then we prove the continuous dependence with respect to the initial data and source term for the strong solution in energy norms. Finally, we show the propagation of regularity for global weak solutions. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free