  This paper has been withdrawn by the authors. We consider the
attraction-repulsion chemotaxis system (3 complicated PDEs system) under
homogeneous Neumann boundary conditions in a bounded domain {\Omega} with
smooth boundary, then the classical solutions to the system are
uniformly-in-time bounded. After the local existence and uniqueness of
solutions was proved, some priory estimates and proves will be established for
the global existence of solutions (see the complete abstract in the PDF version
of paper).
