Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces

The paper deals with the analysis of a model multi-component fluid admitting chemical reactions. flow is considered in incompressible regime. main result shows global existence regular solutions under assumption suitable smallness conditions. In order to control special structure condition on derivatives production functions determining reactions required. shown new critical functional framework Lorentz spaces type $$L_{p,r}(0,T;L_q)$$ , which allows integral $$\int _0^\infty \Vert \nabla u(t)\Vert _{\infty } dt$$ .