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 nonlinear SchrÃ¶dinger 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.
UR - http://preprints.sissa.it/handle/1963/35294
U1 - 35600
U2 - Mathematics
ER -