Weighted Energy Methods in Fluid Dynamics and Elasticity Introductory topics on stability of viscous flows Energy methods in unbounded domains: The case of a half space Energy methods in unbounded domains: The case of an exterior domain Some properties of steady solutions in exterior domatins Exchange of stabilities symmetry and the connection between linear and nonlinear stability Skew symmetric operators and nonlinear stabilization: The hydromagnetic bénard problem Weighted energy methods in elastostatics on unbounded domains Weighted energy methods in linear elastodynamics in unbounded domains.