This paper deals with an extension of a previous work [Gravitation & Cosmology, Vol. 4, 1998, pp. 107-113] to exact spherical symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of, taking into account their own gravitational field. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the Einstein and spinor field equations with a power nonlinearity has regular solutions with spinor field localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor field equations are also obtained in flat space-time.
Abstract.We consider the problem of convective heat transport in the incompressible fluid flow and the motion of the fluid in the cylinder which is described by the Navier-Stokes equations with the heat equation.The exact solutions of the Navier-Stokes equations, the temperature field and the vorticity vector are obtained.
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