In this thesis we study two different problems of mathematical physics. In the first part of the thesis we discuss some questions related to the partial regularity theory of the Navier-Stokes equations. In particular, we obtain some summabilities properties of the pressure field associated to a Hopf weak solution and we give an existence theorem for suitable weak solutions; moreover, we prove that a Hopf weak solution which satisfies a suitable extra-condition, is a suitable weak one too and we consider the question of Hausdorff dimension of the possible singular set S of the weak solution. In the second part of the thesis we study the asymptotic stability of solitary waves solutions for the Maxwell-Schrödinger system
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