Some Exact Solutions to Equations of Motion of an Incompressible Third Grade Fluid

This investigation deals with some exact solutions of the equations governing the steady plane motions of an incompressible third grade fluid by using complex variables and complex functions. Some of the solutions admit, as particular cases, all the solutions of Moro et al[1].Comment: 6 pages, 7 figure

On nonlinear stability of MHD equilibrium figures

.The problem of equilibrium figures of electro-conducting fluids is studied. It is set the initial boundary value problem for the equations governing both incompressible and compressible flows of electrically conducting fluids with unknown free surface. Next it is introduced a new criterion of nonlinear stability of rest state of a heavy electro-conducting, incompressible or compressible fluid in a section of horizontal layer with rigid plane bottom, and upper unknown free boundary in the vacuum. Such criterion proposes an alternative definition of perturbation, and is deeply relied to the unknown motion of the boundary. Finally, it is proved nonlinear stability, in the class of global regular solutions, if the system has non significant magnetic susceptibility, in absence of surface currents, for large initial data. Kinematic viscosity, magnetic diffusivity, surface tension are only non negative