  This work concerns with the non-local Cahn Hilliard Brinkman system with
singular potential for well-posedness. The results are obtained by
approximating the singular potential by a sequence of regular potentials as
well as introduction of a sequence of a mobility term to remove the blow-up and
pass to the limit in both sequences to establish existence of a weak solution
using Galerkin method. Further we prove the existence of a strong solution
under higher regularity assumptions on the initial data and a uniqueness of the
solution using weak strong uniqueness technique and continuous dependence of
the solutions on the initial data. The existence and regularity results for
solution to the non-local CHB system established in this paper are important
stepping stones to study the optimal control problem constrained by this
system.

Analysis of PDEs;Optimization and Control