  The paper deals with analysis of a model of a multi-component fluid admitting
chemical reactions. The flow is considered in the incompressible regime. The
main result shows global existence of regular solutions under assumption of
suitable smallness conditions. In order to control the solutions a special
structure condition on the derivatives of chemical production functions
determining the reactions is required. The existence is shown in a new critical
functional framework of Lorentz spaces of type $L_{p,r}(0,T;L_q)$, which allows
to control the integral $\int_0^\infty \|\nabla u(t)\|_{\infty} dt$.
