| Abstract: |
| This talk presents several examples of a remarkable stabilizing phenomenon. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When Navier-Stokes is coupled with the magnetic field in the magneto-hydrodynamics system, solutions near a background magnetic field are shown to be always global in time. The magnetic field stabilizes the fluid. In all these examples the systems governing the perturbations can be converted to damped wave equations, which reveal the smoothing and stabilizing effect. |
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