The global attractor for the Navier-Stokes equations in 2D unbounded domains

Ning Ju, Caltech, Control & Dynamical Systems

We will discuss some recent results on the existence of the global attractor for the 2D NSEs on some unbounded domains. Focus will be on the asymptotic compactness with the energy equation, an idea originated from J. Ball, while the weighted space method will be mentioned too. A result improving that of R. Rosa's will be sketched showing that if the forcing term is in the solenoidal space H, then the global attractor is not only compact in L2 but also in H1 space. New difficulty comes from the fact that the nonlinear term of the NSEs does NOT disappear from the enstrophy equation, while it does in the energy equation.