In this paper we study the Cauchy problem for the Landau Hamiltonian
wave equation, with time dependent irregular (distributional) electromagnetic
field and similarly irregular velocity. For such equations, we describe the notion of
a ‘very weak solution’ adapted to the type of solutions that exist for regular coef-
ficients. The construction is based on considering Friedrichs–type mollifier of the
coefficients and corresponding classical solutions, and their quantitative behaviour
in the regularising parameter. We show that even for distributional coefficients,
the Cauchy problem does have a very weak solution, and that this notion leads to
classical or distributional type solutions under conditions when such solutions also
exist.