TY - RPRT
T1 - Global, finite energy, weak solutions for the NLS with rough, time-dependent magnetic potentials
Y1 - 2017
A1 - Paolo Antonelli
A1 - Alessandro Michelangeli
A1 - Raffaele Scandone
AB - We prove the existence of weak solutions in the space of energy for a class of non-linear SchÃ¶rdinger equations in the presence of a external rough 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 regularization 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 suffcient compactness properties in order to produce a global-in-time finite energy weak solution to our original problem.
UR - http://preprints.sissa.it/handle/1963/35294
U1 - 35600
U2 - Mathematics
ER -