Well-posedness of Solutions for a Double-Diffusive Convection System with Anisotropic Non-Newtonian Operators and Damping Terms

This paper investigates the initial-boundary value problem for a double-diffusive convection system that incorporates anisotropic non-Newtonian operators and damping terms in a smooth bounded domain Ω ⊂ R 3 . The primary goal of this work is to establish the existence of weak solutions for this system. To achieve this, we first construct approximate solutions utilizing the Galerkin method. Subsequently, uniform estimates for these approximations are derived through an energy method. Finally, by combining compactness and monotonicity arguments, we prove the existence of weak solutions for the problem.