Abstract: The hyperbolic Navier-Stokes contains an extra double time-derivative term while the hyperbolic MHD differs from the standrad MHD by a double time-derivative term in the magnetic field equation. The appearance of these terms is not an artifact but reflects basic physics laws. Mathematically the global regularity problem on these hyperbolic equations is extremely difficult. In fact, even the $L^2$-norm of solutions to the 2D equations are not known to be globally bounded in the general case. This talk presents recent results on the global well-posedness of the hyperbolic MHD and Navier-Stokes equations, and their convergence to the corresponding MHD and Navier-Stokes equations.
