The paper presents an analysis of classical mathematical models of continuum mechanics, the advantages and disadvantages of their presentation in integral or differential form for computation. All continuum mechanics is based on ignoring the non-integral term obtained after integration on parts in the transition from integrals over the surface to the integral over the volume and symmetries of the stress tensor in laws of conservation. A new mathematical model is proposed that takes into account the non-integral term that is responsible for the influence of the action of the angular momentum and includes the equation of state. Outside, the integral term is related to the circulation of velocity over the volume, i.e., with angular momentum. Differential equations are proposed that are built taking into account this factor. The influence of the final mean free paths and the final time between collisions of molecules on the accuracy of the representation of derivatives through the distribution function is determined.