Mathematical analysis demonstrates weak solution existence for generalized Boussinesq systems with viscous dissipation, proving solution sets remain compact.
Key Points
Weak solutions exist for 3D steady-state generalized Newtonian fluid flows incorporating viscous dissipation without requiring smallness assumptions on data.
The complete set of weak solutions forms a compact topological space, and every solution within this bounded Lipschitz domain satisfies exact energy equalities.
Theoretical analysis uses d-monotone operators and the Leray–Schauder alternative, establishing solvability for strongly nonlinear generalized Boussinesq systems.