Interior gradient estimate for steady flows of electrorheological fluids. (October 2020)

• Record Type: Journal Article
• Authors: Sin, Cholmin
• Is Part Of: Nonlinear analysis. Volume 55(2020)
• Publication Date: 2020-10
• Subjects: Calderón–Zygmund estimate -- Optimal regularity -- Electrorheological fluid -- Variable exponent -- Non-Newtonian fluid; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103138
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we consider the equations of stationary motion of electrorheological fluids in any dimension n ≥ 2 . We show that the first gradient of local solutions to the system has optimal L q -regularity with some q > 1 with respect to the one of the external force. This is achieved by comparison principle and a good λ -estimate.