.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.
On nonlinear stability of MHD equilibrium figures
PADULA, Mariarosaria
2009
Abstract
.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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
