Nonlinear stability of cylindrical configurations with free boundaries is studied for electro-conducting fluids. First, the initial boundary value problem is correctly set for the full system governing flows of incompressible, electrically conducting fluids in Ωt with unknown free surface. Notice that when the domain Ωt exterior to the fluid is a dielectric or the vacuum, also the electromagnetic field in Ωt becomes an unknown parameter of the problem. Second a nonlinear stability criterion for the rest state of an electro-conducting, incompressible fluid confined in a section of a right cylinder with lateral free boundary in the vacuum is proposed. This criterion proposes an alternative definition of perturbation, and is deeply relied to the unknown motion of the boundary. Third, if the fluid has nonsignificant magnetic susceptibility, in the presence of not too large surface currents, for large initial data, nonlinear stability is proved in a suitable class of global regular solutions. Kinematic viscosity, magnetic diffusivity, surface tension may be only non-negative in the absence of surface currents. © 2011 Taylor & Francis.
On nonlinear stability of linear pinch
PADULA, Mariarosaria
2011
Abstract
Nonlinear stability of cylindrical configurations with free boundaries is studied for electro-conducting fluids. First, the initial boundary value problem is correctly set for the full system governing flows of incompressible, electrically conducting fluids in Ωt with unknown free surface. Notice that when the domain Ωt exterior to the fluid is a dielectric or the vacuum, also the electromagnetic field in Ωt becomes an unknown parameter of the problem. Second a nonlinear stability criterion for the rest state of an electro-conducting, incompressible fluid confined in a section of a right cylinder with lateral free boundary in the vacuum is proposed. This criterion proposes an alternative definition of perturbation, and is deeply relied to the unknown motion of the boundary. Third, if the fluid has nonsignificant magnetic susceptibility, in the presence of not too large surface currents, for large initial data, nonlinear stability is proved in a suitable class of global regular solutions. Kinematic viscosity, magnetic diffusivity, surface tension may be only non-negative in the absence of surface currents. © 2011 Taylor & Francis.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
