Abstract: In the follow-up to our analysis of the non-homogeneous
case of the problem in [3], in this paper, we present the analysis of the
homogeneous case, leading to the existence and uniqueness of the solution to
Option A in the statement of the problem as it appears in [2]. As in [3], our
analysis occurs in the space,In this space, we select appropriate test functions with a compact
support in the open bounded domain W. Our analysis differs
to the one proposed by Ladyzhenskaya in [7], in the selection of some function
spaces. Obviously, our test functions are ‘candidates’ for a ‘weak’
solution (in the sense of distributions), to the problem. Using ‘energy
methods’, and some results from our previous research papers, we proceed to
confirm the existence and uniqueness of the ‘weak’ solution to Option A of
the problem as communicated in [2].
Keywords and phrases: sixth problem, millennium, existence and uniqueness, solution.
