Global well-posedness and L2 decay estimate of smooth solutions for the 3-D incompressible Navier–Stokes–Allen–Cahn system

Article type: Research Article

Authors: Huo, Wenwen^a | Teng, Kaimin^b | Zhang, Chao^{c; *}

Affiliations: [a] School of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China | [b] School of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R. China | [c] School of Mathematics and Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We consider the Cauchy problem for the 3-D incompressible Navier–Stokes–Allen–Cahn system, which can effectively describe large deformations or topological deformations. Under the assumptions of small initial data, we study the global well-posedness and time-decay of solutions to such system by means of pure energy method and Fourier-splitting technique.

Keywords: Navier–Stokes–Allen–Cahn, global well-posedness, time-decay, Fourier-splitting

DOI: 10.3233/ASY-241901

Journal: Asymptotic Analysis, vol. 139, no. 1-2, pp. 89-109, 2024