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This work is devoted to the analysis of strong solutions to theAbels-Garcke-Gr\"{u}n (AGG) model in three dimensions. First, we prove theexistence of local-in-time strong solutions originating from an initial datum$(\mathbf{u}_0, \phi_0)\in \mathbf{H}^1_\sigma \times H^2(\Omega)$ such that$\mu_0 \in H^1(\Omega)$ and $|\overline{\phi_0}|\leq 1$. For the subclass ofinitial data that are strictly separated from the pure phases, thecorresponding strong solutions are locally unique. Finally, we show a stabilityestimate between the solutions to the AGG model and the model H. These resultsextend the analysis achieved by the author in {\it Calc. Var. (2021) 60:100} tothree dimensional bounded domains.

Existence and Stability of Strong Solutions to the Abels-Garcke-Gr\"{u}n model in Three Dimensions