Uniform regularity of the weak solution to higher-order Navier-Stokes-Cahn-Hilliard systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Pan, Jiaojiao¹  Xing, Chao²  Luo, Hong^1,3 

[1] Sichuan Normal Univ, Sch Math Sci, Chengdu 610068, Sichuan, Peoples R China

[2] Sichuan Univ, Coll Math, Chengdu 610065, Sichuan, Peoples R China

[3] Sichuan Normal Univ Chengdu, VC & VR key Lab Sichuan Provence, Chengdu 610068, Sichuan, Peoples R China

关键词: Regularity;    Higher-order;    Navier-Stokes-Cahn-Hilliard system;    Energy estimates;   

DOI  :  10.1016/j.jmaa.2020.123925

来源: Elsevier

【 摘 要 】

Higher-order Navier-Stokes-Cahn-Hilliard system is a noted interface system that describes the evolution of two immiscible incompressible fluids. Regularity of the solutions to this system is a primary issue from a mathematical point of view. The purpose of this paper is to improve the known results regarding the regularity with respect to time of weak solutions to two-dimensional higher-order Navier-Stokes-Cahn-Hilliard system. Namely, (H-1, H-k)-regularity of the first and second derivatives of the weak solutions to two-dimensional higher-order Navier-Stokes-Cahn-Hilliard system is obtained with the methods of energy estimates. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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