[1] Abidi H, Gui G, Zhang P. On the decay and stability of global solutions to the 3D inhomogeneous Navier-Stokes equations. Comm Pure Appl Math, 2011, 64:832-881 [2] Abidi H, Gui G, Zhang P. On the wellposedness of three-dimensional inhomogeneous Navier-Stokes equations in the critical spaces. Arch Ration Mech Anal, 2012, 204:189-230 [3] Amrouche C, Girault V. Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension. Czechoslovak Math J, 1994, 44:109-140 [4] Boldrini J L, Rojas-Medar M A, Fernández-Cara E. Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids. J Math Pures Appl, 2003, 82:1499-1525 [5] Braz e Silva P, Cruz F W, Loayza M, Rojas-Medar M A. Global unique solvability of nonhomogeneous asymmetric fluids:A Lagrangian approach. J Differential Equations, 2020, 269:1319-1348 [6] Braz e Silva P, Cruz F W, Rojas-Medar M A. Vanishing viscosity for nonhomogeneous asymmetric fluids in $\mathbb{R}^3$:the L2 case. J Math Anal Appl, 2014, 420:207-221 [7] Braz e Silva P, Cruz F W, Rojas-Medar M A. Semi-strong and strong solutions for variable density asymmetric fluids in unbounded domains. Math Methods Appl Sci, 2017, 40:757-774 [8] Braz e Silva P, Cruz F W, Rojas-Medar M A. Global strong solutions for variable density incompressible asymmetric fluids in thin domains. Nonlinear Anal Real World Appl, 2020, 55:103125 [9] Braz e Silva P, Cruz F W, Rojas-Medar M A, Santos E G. Weak solutions with improved regularity for the nonhomogeneous asymmetric fluids equations with vacuum. J Math Anal Appl, 2019, 473:567-586 [10] Braz e Silva P, Fernández-Cara E, Rojas-Medar M A. Vanishing viscosity for non-homogeneous asymmetric fluids in $\mathbb{R}^3$. J Math Anal Appl, 2007, 332:833-845 [11] Braz e Silva P, Friz L, Rojas-Medar M A. Exponential stability for magneto-micropolar fluids. Nonlinear Anal, 2016, 143:211-223 [12] Braz e Silva P, Santos E G. Global weak solutions for variable density asymmetric incompressible fluids. J Math Anal Appl, 2012, 387:953-969 [13] Chen D, Ye X. Global well-posedness for the density-dependent incompressible magnetohydrodynamic flows in bounded domains. Acta Math Sci, 2018, 38B(6):1833-1845 [14] Choe H J, Kim H. Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids. Comm Partial Differential Equations, 2003, 28:1183-1201 [15] Craig W, Huang X, Wang Y. Global wellposedness for the 3D inhomogeneous incompressible Navier-Stokes equations. J Math Fluid Mech, 2013, 15:747-758 [16] Cruz F W, Braz e Silva P. Error estimates for spectral semi-Galerkin approximations of incompressible asymmetric fluids with variable density. J Math Fluid Mech, 2019, 21:2 [17] Danchin R, Mucha P B. The incompressible Navier-Stokes equations in vacuum. Comm Pure Appl Math, 2019, 72:1351-1385 [18] Eringen A C. Theory of micropolar fluids. J Math Mech, 1966, 16:1-18 [19] Eringen A C. Microcontinuum Field Theories. I:Foundations and Solids. New York:Springer-Verlag, 1999 [20] Friedman A. Partial Differential Equations. New York:Dover Books on Mathematics, 2008 [21] Gilbarg D, Trudinger N S. Elliptic Partial Differential Equations of Second Order. Berlin:Springer-Verlag, 2001 [22] Kim H. A blow-up criterion for the nonhomogeneous incompressible Navier-Stokes equations. SIAM J Math Anal, 2006, 37:1417-1434 [23] Li H, Xiao Y. Local well-posedness of strong solutions for the nonhomogeneous MHD equations with a slip boundary conditions. Acta Math Sci, 2020, 40B:442-456 [24] Lions P L. Mathematical Topics in Fluid Mechanics, Vol I:Incompressible Models. Oxford:Oxford University Press,1996 [25] Lukaszewicz G. On nonstationary flows of incompressible asymmetric fluids. Math Methods Appl Sci, 1990, 13:219-232 [26] Lukaszewicz G. Micropolar Fluids. Theory and Applications. Baston:Birkhäuser, 1999 [27] Paicu M, Zhang P. Global solutions to the 3-D incompressible inhomogeneous Navier-Stokes system. J Funct Anal, 2012, 262:3556-3584 [28] Paicu M, Zhang P, Zhang Z. Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density. Comm Partial Differential Equations, 2013, 38:1208-1234 [29] Simon J. Nonhomogeneous viscous incompressible fluids:existence of velocity, density, and pressure. SIAM J Math Anal, 1990, 21:1093-1117 [30] Struwe M. Variational methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, 4th ed. Berlin:Springer-Verlag, 2008 [31] Tang T, Sun J. Local well-posedness for the density-dependent incompressible magneto-micropolar system with vacuum. Discrete Contin Dyn Syst Ser B, doi:10.3934/dcdsb.2020377 [32] Ye Z. Remark on exponential decay-in-time of global strong solutions to 3D inhomogeneous incompressible micropolar equations. Discrete Contin Dyn Syst Ser B, 2019, 24:6725-6743 [33] Zhang P, Zhu M. Global regularity of 3D nonhomogeneous incompressible micropolar fluids. Acta Appl Math, 2019, 161:13-34 |