Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings

• Published in: Nonlinear analysis: real world applications Vol. 77; p. 104049
• Main Authors: Tran, Minh-Phuong, Nguyen, Thanh-Nhan, Nguyen, Hong-Nhung
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2024
• Subjects: Asymptotically regular problem; Fractional maximal operators; Generalized Lorentz spaces; Regularity; Stokes system; ψ-Morrey spaces; Asymptotically regular problem; Stokes system; Regularity; Fractional maximal operators; ψ-Morrey spaces; Generalized Lorentz spaces
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2023.104049

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving p-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymptotically regular problems, whose nonlinearity satisfies a particular structure near infinity. For such Stokes-type systems, we derive regularity estimates for both velocity gradient and its associated pressure in two special classes of function spaces: the generalized Lorentz and ψ-generalized Morrey spaces.