摘要：

      This talk presents a non-autonomous random framework for inviscid limit problems of two-dimensional stochastic undamped Navier–Stokes, Euler and MHD equations on R^2. By developing and combining the DiPerna–Lions renormalization theory (Invent. Math. 1989), Ball's energy method (Discrete Contin. Dyn. Syst. 2004), and the Krylov–Bogoliubov construction method (Ann. of Math. 1937), we establish: 1) H^1-energy identities for an arbitrary selection of weak solutions; 2) the existence of strongly compact attractors and their inviscid upper semicontinuity in H^1; 3) the existence of invariant measures supported on the attractors, their weak upper-limit inclusion relations in the inviscid limit, and the relation between the geometric semidistance of attractors and the statistical semidistance of invariant measure sets; and 4) a new trajectory-level statistical dissipation theory on complete trajectory spaces in the non-autonomous random setting, together with a Constantin–Ramos–Wagner type (Comm. Math. Phys. 2007; 2024) long-time-first vanishing result.