Reacting Multi-component Fluids: Regular Solutions in Lorentz Spaces

The paper deals with the analysis of a model of a multi-component fluid admitting chemical reactions. The flow is considered in the incompressible regime. The main result shows the global existence of regular solutions under the 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 Lp,r(0,T;Lq), which allows to control the integral ∫∞0∥∇u(t)∥∞dt.