Attractors Of Higher-Order Anisotropic Allen-Cahn-Navier-Stokes Systems

As a model describing fluid flow in physics,the Allen-Cahn-Navier-Stokes systems plays a very important role in fluid mechanics.In this thesis,attractors of higher-order anisotropic Allen-Cahn-Navier-Stokes systems are studied.The main contents of this thesis are as follows.In Part 1,the existence of weak solutions of higher-order anisotropic Allen-Cahn-NavierStokes systems is obtained through the Galerkin approximation method.In addition,the uniqueness of weak solutions of the systems is obtained by using energy estimates.In Part 2,the existence of global attractor of higher-order anisotropic Allen-Cahn-NavierStokes systems is obtained by proving the existence of dissipative continuous semigroups and compact absorbing set in corresponding space.In Part 3,the exponential attractor of higher-order anisotropic Allen-Cahn-Navier-Stokes systems is obtained by using the uniqueness of weak solutions and some energy estimates in the global attractor.