THE EXISTENCE OF THE GLOBAL ATTRACTOR FOR 2D g-Bénard PROBLEM

Tóm tắt

We consider the initial boundary value problem for 2D g-Bénard equations in a
bounded domain with homogeneous Dirichlet boundary conditions. After studying the wellposedness of the problem, one is interested in asymptotic behavior of solutions when time is large
or tends to infinity, as it allows us to understand and eventually predict the development trends of
such systems in future, then we can make the appropriate adjustments to achieve the desired
results. Specifically, for each given orbit of the system and an arbitrary time interval T, we can
find an orbit lying on the global attractor whose behavior when the time is large enough of these
two orbits is small enough in difference throughout the length T. In the paper, we study the
existence of the global attractor of the 2D g-Bénard equations. This is a compact invariant set,
which contains much information about the asymptotic behavior of solutions. Our results extend
some outcomes by T.Q. Thinh and L.T. Thuy in Hnue journal of science (2020)