Blow-up of Weak Solutions of the Cauchy Problem for (3+1)-Dimensional Equation of Plasma Drift Waves

A (3+1)-dimensional equation of plasma drift waves perturbed by a singular potential in an infinite parallelepiped

“…which describes drift waves in a magnetically active plasma (see [9] for a detailed derivation of equation (1.3)).…”

“…By means of a comparison principle, existence and nonexistence results have been obtained. In [9], equation (1.3) has been investigated in the case Ω = R 3 . Namely, the authors proved that for 1 < p ⩽ 3, the Cauchy problem has no weak solution even locally in time, while, for 3 < p ⩽ 5, a global-in-time weak solution does not exist even for small (nonzero) initial functions.…”