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A Rotated Multiplier Applied to the Controllability of Waves, Elasticity, and Tangential Stokes Control

A new family of multipliers with rotated direction is introduced. This technique is applied to obtain new results concerning controllability of waves, elasticity, and Stokes equations. The boundary exact controllability for the wave equation and the dynamic elasticity system is reviewed generalizing the classical exit condition in the case of explicit observability constants. Approximate controllability for the Stokes system is also studied using a boundary control acting only on the tangential component of the velocity. A geometric sufficient condition of exit generalized type is deduced.