  I adapt the Gauge String, representing the strong coupling (SC) expansion in
the continuous D>=3 Yang-Mills theory (YM_{D}) with a sufficiently large bare
coupling constant \lambda>\lambda_{cr} and a fixed ultraviolet cut off \Lambda,
to the analysis of the regularized Wilson's loop-averages. When generalized to
describe the fat (rather than infinitely thin) flux-tubes, the pattern of thus
modified U(N) Gauge String is proved to be consistent with the chain of the
judiciously regularized U(N) Loop equations. In particular, we reveal the
dimensional reduction YM_{D}=>YM_{2}, taking place in the extreme SC limit
\lambda=>\infty, and compare it with the implications of the AdS/CFT
correspondence conjecture. On the other hand, for the loop-averages associated
to the sufficiently large minimal areas, the proposed stringy pattern is
supposed to be in the one infrared universality class (provided the loops are
without zig-zag backtrackings) with the novel implementation of the noncritical
D-dimensional Nambu-Goto string. The peculiarity is due to the nonstandard
\Lambda^{2}-scaling, \Lambda^{2}=O(\sigma_{ph}), of the physical string tension
\sigma_{ph}. Being well-motivated from the viewpoint of the standard YM_{4}
theory with \lambda=>0, this scaling is argued to entail that the considered
modification of the Nambu-Goto system is in the stringy (rather than in the
branched polymer) regime. In sum, the confinement in the continuous D>=3 U(N)
(and, similarly, SU(N)) gauge theory is justified, for the first time, at least
when both N and \lambda are sufficiently large. As a by-product, when continued
to N=1, the Gauge String is shown to describe the continuous U(1) gauge theory
with the monopoles.
