01283nas a2200169   4500008004100000022001400041245010100055210006900156260000800225300000700233490000700240520074700247100002100994700002901015700002301044856004601067       2018                        eng d  a1420-903900aGlobal, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials0 aGlobal finite energy weak solutions for the NLS with rough timed  cMar  a460 v693 a<p>We prove the existence of weak solutions in the space of energy for a class of nonlinear Schrödinger equations in the presence of a external, rough, time-dependent magnetic potential. Under our assumptions, it is not possible to study the problem by means of usual arguments like resolvent techniques or Fourier integral operators, for example. We use a parabolic regularisation, and we solve the approximating Cauchy problem. This is achieved by obtaining suitable smoothing estimates for the dissipative evolution. The total mass and energy bounds allow to extend the solution globally in time. We then infer sufficient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.</p>1 aAntonelli, Paolo1 aMichelangeli, Alessandro1 aScandone, Raffaele  uhttps://doi.org/10.1007/s00033-018-0938-5