Strong unique continuation property and limiting absorption principle for partial differential systems with their applications

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We investigate properties of solutions to system of equations including the Dirac equation which described the relativistic particles like electrons. In particular we establish that the Dirac equation with potential homogeneous of degree zero has only absolutely continuous spectra and it has no bound states if the velocity of light is large enough. Moreover we prove that the Stokes equation in fluid mechanics has strong unique continuation property even if its coefficients have strong singularities with critical order.