Influence of velocity curl on conservation laws

The paper discusses impact of the velocity curl on some conservation laws in the gravitational field and electromagnetic field, by means of the characteristics of quaternions. When the velocity curl can not be neglected, it will cause the predictions to departure slightly from the conservation laws, which include mass continuity equation, charge continuity equation, and conservation of spin, etc. And the scalar potential of gravitational field has an effect on the speed of light, the conservation of mass, and conservation of charge, etc. The results explain how the velocity curl influences some conservation laws in the gravitational field and electromagnetic field.