On the global existence solution for a chemotaxis model

This paper has been withdrawn by the authors.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).