The evolution of a mixture of two incompressible and (partially) immiscible fluids is here described by Ladyzhenskaya–Navier–Stokes type equations for the (average) fluid velocity coupled with a convective Cahn–Hilliard equation with a singular (e.g., logarithmic) potential. The former is endowed with no-slip boundary conditions, while the latter is subject to no-flux boundary conditions so that the total mass is conserved. Here we first prove the existence of a weak solution in three-dimensions and some regularity properties. Then we establish the existence of a weak trajectory attractor for a sufficiently general time-dependent external force. Finally, taking advantage of the validity of the energy identity, we show that the trajectory attractor actually attracts with respect to the strong topology.
Analysis of a Cahn–Hilliard–Ladyzhenskaya system with singular potential
BOSIA, STEFANO
2012-01-01
Abstract
The evolution of a mixture of two incompressible and (partially) immiscible fluids is here described by Ladyzhenskaya–Navier–Stokes type equations for the (average) fluid velocity coupled with a convective Cahn–Hilliard equation with a singular (e.g., logarithmic) potential. The former is endowed with no-slip boundary conditions, while the latter is subject to no-flux boundary conditions so that the total mass is conserved. Here we first prove the existence of a weak solution in three-dimensions and some regularity properties. Then we establish the existence of a weak trajectory attractor for a sufficiently general time-dependent external force. Finally, taking advantage of the validity of the energy identity, we show that the trajectory attractor actually attracts with respect to the strong topology.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
